K. Blanchard:
Most institutions still don't run background checks on applicants for employment -- let alone applicants for an account relationship! There's no law or regulation that I know of that would prevent your question.
Please work with your institution's legal counsel and draft a written notice of your intent to deny an account relationship to anyone with a financial crime conviction history (not only an arrest and not only felonies) that may include, but is not limited to: any theft crime, fraud, forgery, embezzlement, and money laundering, etc. Then expand this list to meet your specific goals and other needs.
Then add your statement of intent to all account applications and your in-lobby marketing brochures. Add a press release and a media interview and perhaps prevent some criminal activity while impressing your potential client base.
Dana Turner
------------------
Dana Turner
Security Education Systems
danaturner@bankersonline.com
210-310-0212