Baronlando said:

Maybe you're thinking of Star Trek III? (There's an automated female P.A. voice saying "space doors are closed" etc. when they steal the ship.)

Haha! That's a very clever thought. But no, it must be a faulty memory. What's strange is that I remember waiting for that moment, and then being very surprised, and specifically thinking that they must have been unable to find the original voice, and so they stuck something in. Now that seems very silly, but I still can't explain it.