Can a leasing agent take deposit, run a background check and credit score, at tenants cost and not rent ?

My friend and I are looking to move out the nests and have been looking at apartments in CO. We applied, providing them with all our information they asked, such as jobs, salaries and backgrounds. They also took the money for the deposit, to run a background and credit score. Can they ask for a co-signer after they have already run our background and credit scores, because we do not currently make enough to cover there "rent*4" requirement? Or is there a law that requires them to rent to us because they took our money and deposit? If they have to rent to us can you provide me with support to take to them.