My PT-40 has tricycle landing gear and I was wondering when landing in a cross wind and using rudder what happens when the nose wheel touches down will the plane veer off to one side because the wheel turns with the rudder.

You may have to release some rudder input once the nosewheel touches, but not all, depending on how much nosewheel deflection you have. Depending on how strong the x-wind the plane may still weathervane into the wind with the nose on the ground. If you touchdown with the correct sideslip you shouldn't get a drastic yaw once the nose touches, especially since you should be at low speed by the time you bring the nosewheel to the ground.

Release the rudder some just before touchdown.

You should let the rudder go once the plane touches down. Worse case, the plane will steer towards the direction the rudder is being held, which will be the correct way to compensate for the cross-wind. You should let go of steering all together once the plane is tracking down the runway correctly, and only feed in minor adjustments to keep it tracking straight. Although the rudder will move once the front wheel is on the ground as you steer, it won't really do anything.