As a landlord you need to know whether your tenants are going to pay their rent. Getting a tenant into your property is no good to you unless they pay the rent on time, and in full.
That's why you need to make sure you carry out credit checks on them. A credit check looks at your tenant's financial record - how they handle debt, credit cards and bill payment - and it will allow you to assess how likely they are to pay you on time.
After all, if month after month they miss their credit card payments, how likely is it that they will be able to pay you on time?
The very least you need to do to check out a tenant is to get references from their bank and their employer. But while this will show you that they are employed, and how much they earn, it won't show you whether that money will end up paying the rent, or being spent elsewhere.
You might also contact the previous landlord to find out whether they received the rent on time every month.
In the US, individuals are now entitled to inspect their credit records for free once a year. You could ask tenants to provide you with a copy of this credit record. However, bear in mind that it could have been forged or altered if they feel they have something to hide.
Your best option, and one you should certainly take if you are letting out high value property, is to get your tenant professionally checked by one of the agencies that specialize in tenant checking.
A credit check should turn up any bankruptcies, late payments, and court orders against the prospective tenant. It will cost you money, but it is normal practice for landlords to request prospective tenants to fund the check themselves. If a prospective tenant doesn't want to spend the money, that might be a sign that they have a problem - and think they wouldn't pass the check. So just by being a responsible landlord and asking for a credit check, you have saved yourself a problem in future!