In Texas, an employee does not have a right to a copy of one’s personnel file once the employee leaves a job.  It is not that there is a law prohibiting obtaining a copy.  There simply is not a law providing one way or the other.  Texas is an at-will state.  So, if there is no statute, then private employers can do as they please.  

But, if the employee worked for a state, county or local government, the employee could submit a Public Information request pursuant to Texas Government Code Chapter 552.  The Public Information Act is the state equivalent of the Freedom of Information Act.  If the former state, county or local government employee submits a Public Information Act request, then he/she can obtain a copy of his/her personnel file.