Some think so because of NCIS TV show where the NCIS takes over off-base cases.
They do not have authority off -base.
They will work with local police.
Negative Ghost Rider. Persons subject to the UCMJ are under military jurisdiction regardless of their physical location. Yes, those powers are typically (in the US and overseas) exercised in conjunction with local authorities (many installations have formal agreements with local authorities regarding such) so for example and MP town patrol in a bar district frequented by GIs is normally conducted with the local PD. Army MPs, AF Security Forces derive their authority from the installation commander who is tasked with maintaining law and order on the installation and hence their authority is limited to such.
AFOSI, like the Army CID and NCIS are federal agents with both military and civilian special agents in their ranks and their arrest powers differ. Military agents have no authority over civilians. Civilian agents do, and have arrest powers both on and off post.
“They do not have authority off -base.”
That was changed. NCIS CIVILIAN agents are sworn federal law enforcement officers. The military agents are not.