I recently purchased a new construction home. There is a roughed in bathroom in the basement. They marked the spot where the drain for the tub/shower was suppose to be. Well I dug down 3 feet and no sign of a drain. Is it possible to connect the tub/shower drain up to the sink drain.

If you paid for a basement rough in you should get what you paid for. Call your contractor back and force him to complete his work. You may connect the tub/shower drain line to the sinks drain and be wet vented by it. Good luck, Tom