You must complete all the proper portions of the forms that pertains to your situation, send supporting documents to prove that an error has been made, and appropriate fees.

https://www.dshs.texas.gov/vs/reqproc/amendment.shtm

Paternity: By naming a father on the Texas Birth Certificate or on an Acknowledgment of Paternity Form, a presumption of paternity is established for a child born in this state. This should not be confused with establishing a legal father for the purpose of child support or visitation. For information on how to establish a legal father, contact the Texas Office of the Attorney General, or see the Attorney General site on Establishing Paternity. Forms and assistance in adding a father's name to the Certificate may be obtained at the Galveston County Health Districts Vital Statistics Offices 409 938-7221. For additional information, please see the The Office of the Attorney General 1-866-255-2006

Physical Address

Galveston County Health District Vital Statistics
9850-A Emmett F. Lowry Expressway, Suite A-102
Texas City, TX 77591

For out-of-state birth or death certificates

• National Center for Health Statistics

Birth, death, or marriage information that occurred abroad to U.S. citizens may be obtained from:

• The U.S. Department of State
  1111 19th Street NW Suite 510
  Washington DC 20524
  Phone: 202-647-0518 or 202-955-0307

Authenticating birth or death certificates (Apostille)

• Texas Secretary of State

Print and fill out Birth/Death Certificate & Notarized Proof of Identification Statement

The following mailing address MUST be utilized for overnight delivery:

Galveston County Health District
9850-A Emmett F. Lowry Expy., Suite A114
Texas City, Texas 77591

Send by an Overnight Delivery Service (Not regular mail, priority mail, or certified mail), and enclose a prepaid Overnight envelope. Include money order for the appropriate fee made payable to: Galveston County Health District. Copies are mailed the same day as received.

Some Local Registrar offices, including the Galveston County Health District, have remote access to Texas birth certificates from across the state. Locations of other offices with Remote Access are available from the Galveston County Health District (409) 765-2520, or the Texas Bureau of Vital Statistics, (512) 458-7111 or (888) 963-7111.

http://www.cdc.gov/nchs/w2w.htm

http://www.sos.state.tx.us/authinfo.shtml

http://www.dshs.texas.gov/vs/reqproc/heirloom.shtm

Galveston County Health District has records from 1903 to the present. The Galveston County Clerk's Office has court orders and delay documents, or you may wish to contact the genealogy section of the Texas State Library and Archives Commission.

http://www.cdc.gov/nchs/w2w.htm

Print out, complete and mail the Application For Certified Copy of Birth/Death Certificate & Notarized Proof of Identification Statement.

OR

Include the following information in a letter:

• The name on the birth or death record being requested.
• The date and place of birth or death.
• Father's full name (last, first, middle).
• Mother's full name, including her maiden name.
• Purpose for obtaining the certificate.
• Relationship to the person whose certificate is being requested.
• Your daytime telephone number with area code.
• Your handwritten signature and complete return mailing address.
• A photocopy of your picture ID, such as your driver's license
• A notarized proof of identification statement

You can request certified copies of:

Births

• Births in Galveston County
• Births outside of Galveston County but born in Texas

Deaths

• Deaths in Galveston County

Fees are available at this link.

Apostille: Authenicating Birth or Death Certificates

If you are transferred by your employer to a foreign country, wanting to marry in a foreign country, or if you are adopting a child born in a foreign country, you may need to present your birth certificate to an official with the foreign country. If you are taking a deceased family member to a foreign country, or settling an estate of a deceased family member in a foreign country, the government officials with the foreign country will most likely require the death certificate of the decedent. Depending on the country and the circumstance, the documents may not be accepted by the foreign government officials unless they have been authenticated by the Secretary of State's Office. The 1961 Hague Convention established a pre-printed form for the purpose of authenticating documents for the countries that have joined the convention. This form is called an Apostille. If a document is authenticated with an Apostille, it will be recognized and will not need further certification as long as the foreign country requesting the document has joined the Hague Convention. Since October 15, 1981, the United States has been part of the Convention.

http://www.sos.state.tx.us/authinfo.shtml