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.
And it's more important than ever before to do your background checks. The idea of renting to someone with a horrible history of evictions is bad enough, but it's even more frightening to think you might rent to a criminal with a long rap sheet, or a shady sex offender who might get up to who know what kind of trouble. And these people need some place to live. So they often skip from property to property, hoping the landlord won't do a background check and expose them.
That's why you simply can be too careful, and you can't be to vigilent when it comes to your rental property. The downside is just too high. You can get in a world of trouble if you have the wrong tenant.