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This is called admissibility of illegally obtained evidence in a civil case. The answer is - in Texas at least - is "no." Under Collins v. Collins, 904 S.W.2d 792, 799 (Tex. App. – Houston [1st Dist.] 1995, writ denied), in a custody dispute, the Court ruled that a recording obtained in breach of the law could not be used as evidence for the custody matter:
"Because the tapes were illegally obtained under the federal and state statutes, the trial court should not have admitted them into evidence on the issue of custody. The tape-recorded conversations were not admissible because the criminal statute dealing with the use of the intercepted communications criminalizes their dissemination, and the civil statute provides a method to prevent dissemination. To permit such evidence to be introduced at trial when it is illegal to disseminate it would make the court a partner to the illegal conduct the statute seeks to proscribe." Id.
While this deals with recordings, the precedent (arguably) expands to other evidence gathered illicitly.
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