Don't neglect to check previous landlord references. For liability reasons, some may not be willing to verify anything other that the fact that they did rent there. A good question to ask is, "Would you rent to them again?"
Doc Stephens, REALTOR
Accredited Buyer Representative
Licensed Associate Broker
As Tim suggests; check the internet for on-line credit check services. Here are a couple to try:
Good luck to you!
Prudential Connecticut Realty