Generally speaking, state and municipal police are permitted to exercise their arrest power outside the geography of their jurisdiction, so long as they are in "fresh pursuit" of the suspect apprehended. This is to prevent criminals from simply fleeing across state lines to escape criminal liability for their actions.
What is the definition of "fresh pursuit," and where are its limits either in geography, timeliness, or the like?
Hypothetical if it helps: As part of an investigation into charges of solicitation for prostitution, a police officer - posing as a prospective client - enters a vehicle the suspect is driving without alerting the suspect to the fact that they are a police officer in order to continue to gathering evidence prior to making the arrest.
The evidence that the officer is looking for occurs across state lines. May the officer make the arrest there and then, in the foreign jurisdiction, on the grounds that their investigation constitutes pursuit? Or must they wait until they are driven back to the state they hold jurisdiction in to announce their identity and make the arrest?