Would it be illegal for a fourteen year old to assist the police in solving a murder in New York City? What kind of red tape would the department need to navigate in order to enlist their help?
There are various ways in which a minor cannot assist a police investigation, and it might be useful to say in what ways any civilian could do so (TV shows notwithstanding). A civilian cannot conduct a custodial interrogation, nor can most of them gather physical evidence (so that a proper evidence log is maintained including relevant information on method of collection, the evidence isn't contaminated etc. – stuff that requires a modicum of training). They cannot execute a search warrant.
On the other hand, anyone can provide information that is useful to the police, and it can be done without giving your name or indicating that you are a minor. A minor can serve as a witness at a trial, and it can be helpful to police to know that they have a witness to a crime. A minor can also be used the same way an adult is used, as a confidential informant. There is not a lot of data on that practice given the confidentiality of juvenile records, but there is an article to read ("Juvenile Police Informants: Friendship, Persuasion, and Pretense". The article does suggest that parental consent may be necessary in some cases (such as wearing a wire to a drug transaction).
There is a law in Washington requiring every county's prosecutor to have a local protocol for using informants, and there should be guidelines developed by a work group, however the results (if any) of that group's meetings are not available on the internet. It is possible that there are specific restrictions on the use of minors as informants in some jurisdiction. The article explores the subtle distinction between "informant" and "friend", applied to minors. California has a law that limits the use of minors – none under 15, those above with approval of a judicial officer and parent, though those 13 and older can be used as bait in a cigarette or alcohol sales case.
New York does not have a blanket prohibition against using a minor as an informant, but there may be relevant guidelines for a particular department.
- Short Answer:
They must be a registered informant, with set parameters and only conduct agreed activities.
- Long Answer:
For a juvenile (i.e. someone under 18 years old) to provide proactive assistance to the police in the way suggested by the question, they must be authorised under Part 2, Regulation of Investigatory Powers Act 2000 (RIPA, pronounced ripper) as a Covert Human Intelligence Source (CHIS, rhymes with fizz), or more accurately a JCHIS.
In addition to Part 2, there is the CHIS Code of Practice, and the Regulation of Investigatory Powers (Juveniles) Order 2000 (as amended by the 2018 Order) which, as well as providing for the authorisation and agreed conduct for all registered CHIS, they ceate specific safeguards for a juvenile CHIS.
In particular, the 2000 Order requires:
No authorisation may be granted for the conduct or use of a source if:
(a) the source is under the age of sixteen; and
(b) the relationship to which the conduct or use would relate is between the source and his parent or any person who has parental responsibility for him.
(1) Where a source is under the age of sixteen, the arrangements referred to in section 29(2)(c) of the 2000 Act must be such that there is at all times a person holding an office, rank or position with a relevant investigating authority who has responsibility for ensuring that an appropriate adult is present at meetings to which this article applies.
(2) This article applies to all meetings between the source and a person representing any relevant investigating authority that take place while the source remains under the age of sixteen.
(3) In paragraph (1), “appropriate adult” means:
(a) the parent or guardian of the source or;
(b) any other person who has for the time being assumed responsibility for his welfare or is otherwise qualified to represent the interests of the source.
[succinctly as the content is too long to reproduce here: a comprehensive risk assessment must be in place]
In relation to an authorisation for the conduct or the use of a source who is under the age of eighteen at the time the authorisation is granted or renewed, section 43(3) of the 2000 Act shall have effect as if the period specified in paragraph (b) of that subsection were four months instead of twelve months.
The Act also allows for, in certain circumstances, an authorisation for a CHIS to commit criminal conduct, but I cannot find any example where this has been carried out by a JCHIS.
For completeness, R (Just for Kids Law) v Secretary of State for Home Department  EWHC 1772 (Admin) was a challenge against the lawfulness of using JCHIS. The challenge failed, and the court determined that:
The scheme to authorise juvenile CHIS adequately safeguarded the interest and welfare of juvenile CHIS and did not therefore give rise to an unacceptable risk of breach of the Article 8 rights [i.e. respect for private and family life] of a juvenile CHIS.
In NYC minors need a work permit to work. They can’t work in a factory, they can’t work on cars, their working hours are restricted. So, mainly the kid has to fill out and get the correct paperwork done (at their school) and signed by their guardian. The employer has to keep a copy of certificate.
There could be some problems with firearms, if they want to arm the minor. The requirements for being a NYPD Detective state that you have to be at least 21, I imagine that is policy and not law. Private Investigator has an age limit of 25, which I believe is law.