Tarrant County Courthouse - The State of Texas did not begin requiring birth records until 1903.  Some early records may not exist because was several years before there was full compliance with this new law.  There will be some records on file that predate 1903.  They were filed much later as Delayed Birth Records for various legal reasons, such as to apply for social security.

The Tarrant County Health Dept. keeps birth records on individuals who were born inside the city limits of communities with a population of 2400 or more.

Texas Department of State Health Services. (Texas Vital Statistics)