There are three specific statutes in the Penal Code that provide the authority to grant testimonial immunity in criminal cases. 71.04 (applying to Organized Crime cases), 47.08 (applying to Gambling cases) and 43.06 (applying to Prostitution cases).

Is that the extent of the authority to grant testimonial immunity or do trial courts have a general authority to grant it whenever a witness has relevent testimony but refuses to testify on 5th Amendmant grounds?

Graham v State, 994 S.W.2d 651, 655-56 (Tex.Crim.App. 1999):

"Though a procedure for the granting of immunity has not been expressly provided by the Legislature of this State, in Ex Parte Muncy, 72 Tex.Crim. 541, 163 Page 656 S.W. 29 (1914), the Court made clear that such a procedure was to be recognized."