Didn’t people used to have to have references from previous landlords? Seems like a good idea.
Pull a credit report.
If not references from a previous landlord, at least credit and background checks. I require a credit and background check on every person 18 years of age or older. It also helps if you get the money up front and have them sign a lease agreement BEFORE you turn over the keys.
I actually depend more on credit and complete court/criminal background check than on reference from a current landlord. I have been lied to too many times by a current landlord that is wanting to unload a bad tenant.