Final answer:
A peace officer lacks the jurisdiction to investigate and issue a traffic citation if the incident occurs outside their authorized geographical area or if the matter falls outside of their enforcement authority, such as federal officers dealing with federal laws and not state traffic regulations.
Step-by-step explanation:
A peace officer typically does not have jurisdiction to investigate and issue a traffic citation if the incident occurs outside the geographical area where the officer has authority. For instance, state police have authority to enforce laws statewide and can issue traffic citations on highways, but local or county police are limited to their own town or county. Federal officers, on the other hand, handle specific federal matters and their jurisdiction is linked to federal laws and not state traffic regulations. Therefore, if a crime has not occurred, such as in the case where there is a demand for a citizen's immigration papers without any traffic law violation, the jurisdiction to detain and demand such papers would not typically fall under traffic enforcement authority.
One example of a peace officer not having jurisdiction is when they attempt to enforce laws outside of their specified geographical area or remit, such as a local police officer trying to issue a citation on a federal property where federal law enforcement has jurisdiction.