I am attempting to figure out everything I need to know before operating either an electric or gas-powered bicycle, such as whether I need to get a license or register the bike. Does there exist an authoritative source that I can go to in order to find out as much as I can? I have found the contact information for my local legislative information office. Is this a good place to go in order to find out what I need? Thank you.
TL;DR: it may be extremely difficult to find out.
The title question has an even more complicated answer, but the question about powered bikes is fairly simple (by legal standards). Any laws about bike licensing are at the state or municipal level. I'll take Washington for illustrative purposes. RCW Ch. 35.75 authorizes cities and towns to license bikes, therefore I set my city to be Seattle. A typical approach is to find the web page for the DMV and see what they say. Unfortunately, in Washington that is the Dept. of Licensing, which licenses everything. But one of the most-findable links is for vehicles, then you want registering (getting a license for), and then the useful links end because your choices are "moving to WA", "transferring", "off-road", "military personnel" and "emissions". The one that might be relevant is "transferring" in case you buy the bike from a dealer, or from a private party. The third option, DIY, is not contemplated: if that is the case, don't assume that you're off the hook. But you can save your breath, those links never address the question of motorized bikes.
Option 2 is to try to contact the Department of Licensing and simply ask them. This is not likely to give you an authoritative answer, and if you do it by going to the local licensing agency, it's likely to give you no useful information (they primarily process papers). A written letter to the DOL requesting legal citation of DOL regulations and state statutes might yield something that you can look up.
Option 3 is to Google it, good luck there. In every state, there is some law that requires vehicles to be licensed, and finding that section of the law is the first next step. It may be buried in millions of results of you search for "washington vehicle license law", but if you search "washington vehicle license statute", you get a bunch of pages with titles "RCW so and so": RCW is the abbreviation for "state laws" (statutes). You want Title 46. Now you home in on Registration (NB Washington law is extremely accessible, and everything links to everything, so it might be more challenging in another state. Virtually impossible in New York).
Unfortunately there is still a huge wall of text to read and interpret. I did not know this in advance, but this web page (which appeared above the hit for this) says that motorized bikes are "mopeds". That leads to RCW 46.16A.405 entitled "Campers, mopeds, and wheelchair conveyances", which says
Mopeds are considered vehicles for the purposes of vehicle registration and license plate display. The department, county auditor or other agent, or subagent appointed by the director shall charge the fee required under RCW 46.17.200(1)(a) when issuing an original moped license plate. Mopeds are exempt from personal property taxes and vehicle excise taxes imposed under chapter 82.44 RCW.
Now you need to check all of the definitions to see if a motorized bike is indeed a moped. "Definitions" under RCW Chapter 46.16A yields nothing useful, but "Definitions" under RCW Title 46 yields entries for "Electric-assisted bicycle—Class 1 electric-assisted bicycle—Class 2 electric-assisted bicycle—Class 3 electric-assisted bicycle" which I just happened to see by luck, and "Moped". A moped is
a motorized device designed to travel with not more than three wheels in contact with the ground and having an electric or a liquid fuel motor with a cylinder displacement not exceeding fifty cubic centimeters which produces no more than two gross brake horsepower (developed by a prime mover, as measured by a brake applied to the driving shaft) that is capable of propelling the device at not more than thirty miles per hour on level ground.
If it has a small gas engine it is a moped. How can you interpret the clause "having an electric or a liquid fuel motor with a cylinder displacement not exceeding fifty cubic centimeters which produces no more than two gross brake horsepower (developed by a prime mover, as measured by a brake applied to the driving shaft) that is capable of propelling the device at not more than thirty miles per hour on level ground": does the bold restriction apply to only the phrase "liquid fuel motor" or does it apply to "electric or liquid fuel motor"?
There is a meta-rule of legal interpretation known as the last antecedent rule, which dictates that the bold clause only applies to "liquid fuel motor" (the thing right before the modifying clause). However, that rule of interpretation only applies when a clause is ambiguous, and the only way to get an authoritative determination of ambiguity is to make the wrong assumption, get punished, then sue the government – the courts may or may not agree with your belief. Since an electric motor has no cylinder, the courts will not assume the legislature meant anything so silly, therefore for an electric bike, it is most likely (not guaranteed) that "moped means motorized device designed to travel with not more than three wheels in contact with the ground and having an electric motor", period. Remember that the basic licensing law says "Mopeds are considered vehicles for the purposes of vehicle registration and license plate display": a traditional gas moped clearly requires a license and everybody says so.
Naturally, I assume you have a electric motorized bike, known as an electric-assisted bicycle, and that you are skeptical about the idea that an EAB is a moped (I am). Internal-combustion mopeds are defined in terms of limited power capability (a Harley Hog is not a moped), but that limit is part of the "liquid fuel motor with cylinder displacement" clause which doesn't sensibly apply to electric motors. Therefore an electric moped can have unlimited power capacity? Surely the legislature did not intend that (a claim about legislative intent is another tool in the arsenal of legal interpretation).
You can start the search over to find out about the licensing requirement for EAB's, and you won't find anything that permits using it on the road without a license. Searching "rcw electric-assisted bicycle license" yields two helpful pages: RCW 46.61.710 Mopeds, EPAMDs, motorized foot scooters, personal delivery devices, electric-assisted bicycles, class 1 electric-assisted bicycles, class 2 electric-assisted bicycles, class 3 electric-assisted bicycles—General requirements and operation. That statute starts by saying
No person shall operate a moped upon the highways of this state unless the moped has been assigned a moped registration number and displays a moped permit in accordance with RCW 46.16A.405(2)
(also incidentally, "a moped may not be operated on a bicycle path or trail, bikeway, equestrian trail, or hiking or recreational trail", but EABs are in the bike lanes all the time in Seattle).
There is some info from the state patrol. They say "Not licensable for street use (RCW 46.04.320)", but they also say "They may be operated most places bicycles are allowed such as multipurpose trails or bicycle lanes, provided 'motorized vehicles' are not prohibited. (RCW 46.61.710)". The statement that they are "not licensable for street use" refers to the part that says
"Motor vehicle" excludes: (a) An electric personal assistive mobility device; (b) A power wheelchair; (c) A golf cart, except as provided in subsection (2) of this section; (d) A moped, for the purposes of chapter 46.70 RCW; and (e) A personal delivery device as defined in RCW 46.75.010.
Oops. Notice that the law does not say anything about EABs (also, the reference to mopeds is limited to laws about dealers and manufacturers, but not users).
You may find that you don't need a driver's license, but eventually you won't find anything authoritative that says that no license is required. The state patrol page halfway hints that you can't drive them on the road at all – bad phrasing ("not licensable"?). Generally, the lack of a law requiring a license for an EAB would mean that no license is required. But if an EAB is a moped, a license is required.
In lieu of a court case ruling that an EAB does or does not require a license, all you can do is read all of the laws and try to make sense of them. You could ask the state patrol, but they will tell you what they do, not what the law is (I have never seen an EAB with a license in the Seattle, which suggests that an EAB is not a moped for licensing purposes).
B.B. welcome to LSE. Congratulations for asking such a practical first question.
You've already gotten great and helpful advice: Use the internet's (amazing) online law library to find the relevant legal codes, which you can read through to find the answers to your questions. To do this, just follow the detailed example so helpfully provided by 6726.
You could also take the opposite approach. Instead of using the internet to do your own legal research, you can use the internet to look for experts who've done your research for you! If you are lucky, people who know about the law of electric or motorized bikes in your state will have written up what they know in an easy-to-digest form.
For example, it looks like you are in Alaska, so you could start by searching strings such as: Alaska + electric + bike and "license" or "laws" or "registration" and so on. If you do that, you will find many sites summarizing the legal requirements for you in plain English.
Obviously, since this is the internet, you can't believe everything you read. These sites could be out of date, or the people who wrote them could be confused, or...or... But if you read a several of them, you can usually get a sense of what is going on. And if you are really lucky, you'll hit the jackpot, and find an official website explaining the law clearly and concisely.
I am not against reading statutes, administrative codes or court decisions or other legal materials. I am simply being a realist. Legal materials are important, but they can be hard for non-lawyers to find, read and understand. As 6726 says, the internet helps by making it easy to find them. In many cases, the internet does more: It digests that material for you, so you don't have to spend time trying to parse the various statutes and codes.
If you have car insurance, you might also call your insurance agent. He is likely to know.
Added after comment:
This page from the DMV says you need an M2 permit to operate a "motorized bicycle." I guess the thinking is that by definition an electric motor has an "engine displacement of less than 50cc."