It's legal for a landlord to charge a reasonable fee for running a credit check on a prospective tenant. It's illegal, however, for a landlord to charge such a fee and then not use the money for the purposes of a credit check. Landlords who request such a fee and then don't perform a credit check should return the check to the applicant. Landlords who expect to run numerous credit checks often join one of these reporting agencies. If a credit report shows that a prospective tenant moves frequently, is behind on many debts or has filed for bankruptcy, many landlords will reject the tenant's application.
Some landlords also run criminal record checks on prospective tenants.
The bottom line Landlords can reject possible tenants for any reason they wish as long as it is not for discriminatory reasons. Work with an experienced lawyer in your state.