Texas law to select tenants

[Lei Zhao]

Does Texas law allow screening multiple tenants and select the best one? I've heard from local people that we're only allowed to do the screening one by one and should give the unit to the first one who met the minimum requirement. However, I didn't find this law online. We have a duplex in Fort Worth area which has a tough tenant pool so I would like to screen more tenants if possible. 

[Bruce Lynn]

Who really knows in the end, but I would think if they were the 1st and they met the minimum requirements YOU set, then you might be descriminating.    How would you feel?   If you don't like your minimum requirements, make them more stringent.