Police said Murdoch was cooperating with investigators. He was questioned after his arrest, and Deputy Police Chief Paul Feist said the investigators described him as polite and respectful.
Murdoch's arrest comes just days after Gov. Susana Martinez called on the state's judges and lawyers to take steps to help bolster confidence in the legal system. She cited a case of alleged judicial bribery in Las Cruces in which state District Judge Michael Murphy is accused of telling a potential judicial candidate that she needed to make payments to a Democratic activist if she wanted to be considered for a seat on the bench under then-Gov. Bill Richardson.
The arrest also comes just weeks after former University of New Mexico President Chris Garcia, a respected political science professor, was accused of helping lead a sophisticated online prostitution ring.
Police said there was no connection between the Garcia case and Murdoch.
Associated Press writer Susan Montoya Brown contributed to this report.