Can we discipline an employee for secretly recording workplace conversations?

Q. Some employees discovered that a co-worker has been secretly recording conversations with them and some supervisors. One of them brought it to our attention after he grew suspicious that the employee was digging for information about some employment decisions we had made. Several employees have complained about the invasion of their privacy. The company president’s first reaction was to have the employee arrested, but I’m not sure he broke any laws. Our policies prohibit general harassment, but do not specifically address clandestine recordings. Can we discipline this employee? Should we contact police? ...