If I commit a traffic offense in the city and a city cop observes this, and I then leave the city, can the city officer continue the pursuit, or must they terminate the pursuit at the city limits?
There should be a policy, following GA Code § 35-1-14 (2020) which requires there to be a written pursuit policy (if they don't have a policy, they can lose funding). So you would have to look at the particular jurisdiction. The Georgia Dept. of Public Safety (i.e. State Patrol) has this policy, Atlanta has this policy, and so on. I'll ignore the state patrol given their state-wide jurisdiction, but it would apply to interstate pursuit. It specifically says:
4.1.1 Pursuits are prohibited for the following types of offenses: ...3. Traffic offenses
Athens-Clarke County requires (§6.08.04) that
Pursuits are permitted under the following circumstances: [CLE 41.2.2 a-b]
- When an officer has reasonable grounds to believe the suspect has committed, or is attempting to commit, one of the following felonies: murder; rape or other felonious sex offense; abduction; robbery; felonious assault; arson involving death or serious injury;
- When an officer has reasonable grounds to believe the suspect has committed, or is attempting to commit, a crime which involves the display or use of a firearm, even if such crime is classified as a misdemeanor.
The point is that this is a matter of policy determined by each department, and not situation with a universal answer. In Zilke v. Georgia, the Georgia Supreme Court overturned a traffic conviction because the arresting officer "had no authority to arrest appellant because, at the time of arrest, Officer Mason was outside his statutorily-designated territorial jurisdiction". That case involves a DUI not a speeding ticket and also involved campus police not city police, so different conclusions are still possible for citations rather than arrests. It does however indicate that there are jurisdictional limits to police actions within the state of Georgia.