Apparently, an illegitimate child can’t. The Health and Safety Code §711.004 allows a district court to order an exhumation if requested by certain people including the spouse or the children. That section may not apply to illegitimate children unless money is involved.
In a case decided in 2010, the Texas Supreme Court ruled that a woman who claimed that she was the illegitimate child of a man could not have his body exhumed to test his DNA. The woman asked for the exhumation more than four years after the man’s estate had been closed. The four year statute of limitations applies to making claims for inheritance. The Court said that because she could not claim part of his estate since more than four years had passed, she did not have a “justiciable interest” in the exhumation of his body for DNA testing. 04-0608.
Pearls of wisdom: Apparently, whether you have a father or not is unimportant. You have a “justiciable interest” only if it will lead to money, not peace of mind! In fairness to the Court, the woman was making a claim for her inheritance which the Court ruled was barred. But the broad language of the decision seems to make exhumation for DNA testing a proposition based on money alone.

Does this mean, that in Eliza Presley’s case, where on the grounds of hairs positive DNA tests results, she could not request an exhumation of Vernon Presley’s body, because the estate was long ago distributed?
The case stands for the proposition that if you are too late to contest a will, you don’t have a right to exhume the deceased in order to prove that you are his heir. Whether the court would rule the same way in a case that did not involve a will contest, is unknown.
Thank you Robert.
Do you happen to know what is the period of time, which defines it to be ‘too late to contest a will’ ?
Thanks, Lina
Lina, look at this section of my website: http://theprobate.net/contesting-wills-mainmenu-26/when-to-contest-a-will-mainmenu-33/269-statute-of-limitations.html.