Cops Investigate Shane Gibson

TMZ has learned the Commissioner of Police in the Bahamas has received "an official complaint" against former Minister of Immigration Shane Gibson -- and the Commissioner is now conducting a formal investigation.

Gibson resigned after photos surfaced showing a chummy relationship between himself and Anna Nicole Smith. Gibson green-lit Smith's petition for residency, even though it's questionable she was entitled to receive it.

Police sources would not say who or what agency filed the complaint. We're told, however, that the Commissioner is required to investigate. Sources would not say if the investigation involves possible criminal misconduct.