Last month Sinn Fein's Daithí McKay resigned as North Antrim MLA.
It followed the emergence of details of secret contacts between the former chairman of the Finance Committee, another Sinn Fein member and loyalist blogger Jamie Bryson.
Mr McKay said he accepted this was "inappropriate, ill-advised and wrong".
A separate inquiry into the matter by the Assembly Standards Commissioner Douglas Bain will be suspended in order to avoid any risk of prejudicing an active police investigation.
Mr McKay chaired the committee last year when Mr Bryson used the Assembly's legal privilege to name former First Minister Peter Robinson as so-called "Person A" in relation to the Nama property scandal.
Mr Robinson has said any suggestion that he sought to benefit from the multi million pound property deal is outrageous and wrong.
In a statement, Det Supt Kevin Geddes said: "Detectives from Serious Crime Branch are investigating to see if any offences have been committed. It would be inappropriate to comment further at this time."
Police are investigating allegations a key witness at an Assembly inquiry was coached, in order to see if any offences have been committed.