A/C clutch
Hope you don't have the same problem as my '95 had but here's the description.
The clutch stayed engaged all the time, even with the control turned off or to heater. The only way to defeat the clutch was to unplug it at the compressor.
A lot of searching ended up at the control head in the dash(my '95 has 'standard' control, not the automatic temperature control). The key test was finding constant 12v on the blue wire at the freon low pressure cycling switch whenever the key was on. Your car may have a green wire with white stripe. This freon switch is near the heater blower behind the passenger tire and is in the fat freon line.
Disassembling the dash, I couldn't disconnect the temperature control cable. The service manual diagram of the clip that holds the cable to the 'control head' (the control with the buttons and temp. slider) was inaccurate. I could have pushed a hook up the passenger side of the clip and pushed it toward the driver's side to release the clip. As it was, I broke it and had to do some creative engineering on reinstallation. To the nub of the problem.
Inside the control head there are several diodes and transistors that form a logic circuit to send a 'ground' signal to the ecm when A/C is requested and other on/off information. The transistor that sent the 'ground' signal to the ecm was shorted (always grounded). An ohm meter showed this as well as the peeled banana shape of the exploded transistor. A 69cent Radio Shack replacement worked fine.
Apparently this contro head is viewed as a modular replacement as there is no schematic in the service manual. If you don't have access to electronic trouble-shooting try this place for an entire control head. I've bought from them and liked their service and goods even though they're a scrap yard.
http://www.contemporarycorvette.com/cars.htm
I joined this forum to resolve this and the forum was great help.
You can find the thread by looking at my posts in Feb (I think).
Hope this helps