What are the Autopilot Minimums for a C-172 G1000?
Typically, the aircraft flight manual will identify this. In your particular case (Cessna 172 G1000), it is 200 feet AGL for all approach types.

The C-172 can be fitted with either a Garmin GFC 700, or a Bendix/King KAP 140.

For the GFC 700, it is listed in the aircraft operating limitations:



In the case of the KAP 140, it is listed in the autopilot supplement: