The Cook Islands police commissioner, Pira Wichman, says he is being briefed about a letter of complaint concerning Mark Lyon.
Lyon, a New Zealander who has several convictions to his name, was granted a residency permit by the prime minister, Dr Robert Woonton, who over-rode the recommendations of the immigration service to do so.
Mr Wichman says the letter from the group for concerned citizens wanted to know whether the police were investigating alleged concerns.
"I have to now hear what the heads of division say. It may well be that I'm not able to answer them directly in relation to this letter. For example, if we are having an investigation, it may not be in the public interests for us to divulge that information, I don't know at this stage."