A Texas rental application enables landlords to obtain the background information of lease applicants before authorizing a residential tenancy agreement. The tenant will often be required to pay a non-refundable fee.Applicant's name (as listed on proof of identification). Applicant's former last name (if applicable). E-mail. We offer a free Rental Application form that can be completed online and a Printable Rental Application. A Texas rental application (Form 2003) is an official document the Texas Association of Realtors provides. Get information you need to find the best tenants. Collect house rental applications online with a free Rental Application Form. Easy to customize, embed, and share. The tenant will often be required to pay a non-refundable fee.