2002 210.11(C)(2)
Laundry Branch Circuits. In addition to the number of branch circuits required by other parts of this section, at least one additional 20-ampere branch circuit shall be provided to supply the laundry receptacle outlet(s) required by 210.52(F). This circuit shall have no other outlets.
210.52(F)
Laundry Areas. In dwelling units, at least one receptacle outlet shall be installed for the laundry.
IMO if the outlet is in the laundry room serving laundry equipment, your dryer, then it should be allowed on the same circuit that your washing machine is on according to this statement:
"at least one additional 20-ampere branch circuit shall be provided to supply the laundry receptacle outlet(s)"