If the squeak is happening only when you release the trigger, that sounds like the trigger return spring, which is the same as the trigger guard latch spring. The spring rubbing on the inside of the housing can make a musical squeak. If you listen REALLY closely, you might hear the same squeak as you pull the trigger, but it's probably covered up by the sound of all the other things - including the mainspring - moving at the same time.
A little dry-fire practice (if it's a centerfire gun) will smooth out the tiny bit of roughness that makes the squeak happen, or you can disassemble the gun and put a little heavy oil or light grease on the spring. If you're worried about attracting dust or grit, you can use a dry lube - my favorite for low-pressure lubrication is a bicycle chain lube.