Tenant credit check can be performed various ways. Traditionally individual owners have gone to their local apartment association where as larger properties and property management companies work with tenant screening companies.
10-15 years ago the landlord credit check was not commonly used when renting to a new resident. Even in today's market, many individual owners are not performing a tenant credit check on their prospective renter. This usually comes back to "bite" the landlord when the tenant doesn't pay their rent or seriously damages the rental unit.