We use the right hand. However, we touch the right shoulder first. Also, we hold the thumb and first two fingers together as s sign of belief in the Holy Trinity, and with the last to fingers against the pal together as a sign of belief in the divinity and humanity of Christ.
As someone mentioned above, one might make the Sign of the Cross with the left hand if one is missing the right hand or it is immobile. I can't think of any other reason to do so.