The mere signing of a document is not absolute proof of voluntariness. The motion challenging the voluntariness of the statement would be a Motion to Suppress the statement. Once a motion is made and hearing is held, you will want to focus on things that tend to show that a statement is not voluntary, such as:
Physical duress (prisoner placed in discomfort until he complies)
Unlawful threats (communicated to prisoner, against prisoner or others the prisoner cares about)
Incorrect explanation of rights
At the hearing, the judge would be the trier of fact, deciding whose testimony is true or not, and deciding what conclusions to draw from the testimony accepted as true.
Contact me at 248-399-6930 for a free consultation. You and I do not have an attorney-client relationship formed by our communications on this website. Advice given by me on this website is general advice based on partial information. You should not rely on any advice given without first hiring a lawyer in the area where the case is pending, and providing that lawyer with full information.
A challenge would be based on all the surrounding facts and evidence of both the offense and how the statement was taken. To answer this question without the facts of this case would require trying to cover the universe of possibilities under which a statement can be taken and crimes for which statements are taken. Is this a case based question or academic?