The new ruling faction, led by political heavyweight and president Sharad Pawar, filed the complaint here on Thursday through secretary Niranjan Shah.
The Board of Control for Cricket in India (BCCI), alleging that Dalmiya misappropriated funds during the 1996 World Cup, has made charges of cheating, forgery, criminal breach of trust and criminal conspiracy.
Dalmiya, who headed the Pakistan-India-Lanka Committee (PILCOM) formed to organise the event, is alleged to have siphoned off funds to the tune of around 47,000 dollars from a PILCOM bank account in Kolkata.
Apart from Dalmiya, former secretary Karunakaran Nair, former treasurers Jyoti Bajpai and Kishore Rungta, a secretary at Dalmiya's office and a bank official have also been named in the report.
"We have been requesting for details of accounting transactions but have not got satisfactory answers," Shah said.
"There is no proper record of withdrawals and no valid reason has been given for tranferring money to Cricket Association of Bengal's (CAB) account," he added.
Dalmiya, who has been at the helm of affairs in the CAB for many years, however, dismissed the allegations as 'fake'.
"I can't reply in detail but have furnished all details to them. There is no truth in the allegations and the present board officials only want to malign me," Dalmiya said.
"It is surprising that they have gone to the police when the case is sub-judice," added the former International Cricket Council (ICC) chief.
Both factions have already gone to court over the issue, but filing a complaint with police sets off an official police investigation.
A high court in Kolkata Thursday admitted an appeal from the board against a stay granted by a lower court on a legal notice to Dalmiya to answer charges of financial irregularities.
Meanwhile a defamation case has been filed by the Dalmiya faction against board vice president Lalit Modi.
The two factions were also involved in legal battles before Pawar's faction prevailed in last year's elections.