(CNN) A Pennsylvania man admitted to taking his girlfriend from Pennsylvania to Nevada under the guise of a vacation and then killing her, according to an Allegheny County criminal complaint filed Friday. Police say he then impersonated her through text and social media for roughly two months.

John Chapman, 39, faces charges of kidnapping, obstructing administration of law and criminal use of a communication facility in Pennsylvania, according to the complaint.

Whether Chapman will be charged with murder is up to Nevada, as Pennsylvania lacks jurisdiction, said Bethel Park, Pennsylvania, Police Chief Timothy O'Connor.

Chapman is being held at Allegheny County Jail in Pennsylvania and was denied bail. A preliminary hearing is set for November 21.

CNN has not been able to identify an attorney for Chapman and calls to his family were unanswered Monday.

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