Screening for co-applicants - please advise

[Victoriya Mints]

I am new landlord and would appreciate some advice. I have a young engaged couple with her child who are interested in renting my home. During the showing, they said they can meet the income criteria of 3X/income jointly but her credit score is bad and she asked if I can use /run just his credit score. We talked about signing them as co-applicants on a rental agreement since neither one of them meets criteria individually (he has low income but high credit score and she has sufficient income but low credit score). I am running both of their background checks and income verifications, and his credit score. Legally, can I reject them if they are co-applicants on the lease if they jointly meet my rental criteria? Thanks so much in advance.