A spokesperson for West Yorkshire Police said: “Police in Calderdale have been made aware of an allegation of financial irregularity.
“A criminal investigation has now been launched to examine this allegation, and is in its early stages.
Calderdale Council has also been made aware of the proceedings.
A Calderdale Council spokesperson said: “We are aware of the Police investigation.”
Calderdale councillors have also raised their concerns about the launch of the investigation.
Councillor James Baker leader of Calderdale Liberal Democrats said: “We are calling on Craig Whittaker MP to explain to the people who elected him what has gone on here.
“People deserve transparency and openness from their politicians. We have also called on Calderdale Council to investigate this matter as it implicates both the leader of the Conservative group and the Mayor of Calderdale.”