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.A Texas rental application (Form 2003) is an official document the Texas Association of Realtors provides. Applicant's name (as listed on proof of identification). Applicant's former last name (if applicable). E-mail. Create a free personalized Texas rental application form now to determine the reliability and credibility of potential tenants for your property. 1. Gather all required information regarding applicants. Use our Texas Rental Application to Use to vet prospective tenants. Create an attorney-drafted Rental Application form here. Simplify tenant evaluations with our Rental Application Form Texas.