What type of petition might a suspect file to contest their prolonged imprisonment without being returned to their state of origin?

The correct choice is the petition for a writ of habeas. This legal instrument is specifically designed to challenge the lawfulness of a person's detention or imprisonment. When someone believes they are being held in custody without sufficient legal justification, a writ of habeas can be filed to seek relief from that detention.

In the context of prolonged imprisonment, particularly when a suspect has not been returned to their state of origin, the habeas petition allows them to contest the legality of their confinement. This mechanism ensures that individuals have the right to question whether their detention complies with legal standards, thereby protecting their liberty interests.

Other types of petitions mentioned serve different specific purposes. A petition for a writ of certiorari is typically used to seek judicial review of a lower court's decision by a higher court, not directly addressing wrongful detention. A petition for legislative review involves requesting a legislative body to evaluate and possibly change existing laws or policies, rather than challenging individual imprisonment. Lastly, a petition for a criminal appeal is about contesting a conviction or sentence after a trial, which does not directly relate to the issue of prolonged detention without return to the state of origin.