Asking a professor to supervise research done with a different professor
It is a bad idea for a professor in your department to enroll you for research credit under his supervision without actually supervising. This is taking all the responsibility without any control, contribution to educating the student, or simply a pleasure doing the research.

However, you probably should connect those professors from different departments, so that they determine their shared interest and responsibilities in this project. Between them (and probably the undergraduate advisor) they might determine the formalities to follow department's &amp; programs's regulations; but if somebody's name appears as an advisor of a work, he must actually do some part of advising.