Is it illegal for an employer to require applicants for a job to provide a background check with their resume?

it would not be illegal to specify the service you wish them to use and upon hire you would reimburse them for the check, would cut down on the liars and the cost to you, especially if entry or mid level position, anything higher may turn them off, but a good interview process and reference check can narrow down the people you want to hire before you implement the criminal background check.