According to her entry on Memory Alpha she played the computer in a TAS episode but never in TOS (unless thats incorrect)
Majel Barrett wasn't
credited as the voice of the computer in TOS, be she
was definitely the person who did it. Hence the number of ST novels that have suggested that Number One (of "The Cage") supplied a template of her emotionless voice for the TOS computer.
After Roddenberry tried a male voice in TMP (Doug Hale, IIRC), the producers returned to a female voice for ST III. It wasn't Majel in ST III since she'd withdrawn her support on the ST films due to Gene Roddenberry not being involved beyond the role of figurehead. Teresa E Victor (who did the countdown sequence) was director Nimoy's personal assistant at the time, IIRC.
For TAS, the voice of the ship's computer was sometimes performed by Majel Barrett, but sometimes done by Nichelle Nichols. With only two regular female voices available, it was sometimes necessary to have Nurse Chapel or Uhura talk to the computer.
It wasn't until TNG's "Manhunt" when we had the inevitable, hilarious situation of Majel talking to herself: Lwaxana Troi (Majel) interrogates the holodeck computer, voiced by Majel!