Your '99 has an electric lock and an electric lock release actuator. Your hatch lock is tied in with the rest of the door locks. When in the drivers seat, you can lift the lock lever to unlock all the electric locks. At that point you should be able to go to the hatch and put your fingers in the handle area where you'll feel a little lever. Push that lever to the right and lift. If this doesn't work it means that your electric hatch lock release actuator is broken.

See these message threads for more info, pay particular attention to MY posts in these theads:

hatch stuck

integra electric hatch stuck?

Trunk release inside 2001 Acura Integra???

Good luck with it... it's an easy fix if you're willing to spend the money on the part.

JD