A nonlawyer who is an accountant with an active business has advised me he will refer me clients who have either criminal or civil matters before the district judge. He will then pay me a fee. Is this ethical?

Probably not. Although the question has very few details, it can be inferred that the person or accountant apparently advertises for clients. These clients come into his office and retain the accountant for both legal and accounting issues. The client pays the accountant X number of dollars. The accountant then hires lawyers and pays the lawyer a small portion of the X number of dollars to go to the district court judge’s courtroom for a summary criminal trial or a minor civil hearing.