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It is true, but only to a point. There are two types of privileges.
TESTIMONY IN CRIMINAL CASES: witness spouse may refuse to testify against his/her Defendant spouse. However, the witness spouse can waive that privilege and decide to testify. If so, the Defendant spouse cannot stop them.
TESTIMONY TO COMMUNICATION IN CIVIL AND CRIMINAL CASES: In both criminal and civil cases, communications between spouses during the marriage are privileged if said in a private communication between the two parties. Either party can invoke that privilege and have any such testimony thrown out of court.
These privileges are voided if the spouses are the parties in an action against each other, such as in a divorce or a restraining order.
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