The first question is what kind of autopilot is it, and the second is where is the person located?
I've had good luck with Griffin Avionics at KHYA - Hyannis, MA. They do a good job with the Century/Altimatic units. I wouldn't let them touch any maintenance stuff on my aircraft, but they're the only place I'd take the planes for autopilot work. The Aztec has an Altimatic IIIB, and the 310 has a Century III. Basically they're both the same, with a few minor changes.
Lancaster Avionics (KLNS) has a good shop as well (I'm told), and seems to be good for S-Tec autopilots.
There is enough variability from one unit to another that it's important to pick a place that is experienced with that type. For example, Griffin is the only place I know of that actually is very good with the Century/Altimatic units. S-Tecs seem to be more common and have more places that know how to work with them.