The allegations come days after Kumar, in an explosive letter to BJP's national president Amit Shah, had demanded a 'Lokpal' in the party to tackle the cases of corruption like Vyapam which has "made all of us bow our heads in shame".
During the Lok Sabha polls, Kumar collected funds for BJP and then took it along with him stating that it was meant for him fighting the polls, Kalia, Jalandhar Central MLA, alleged.
"Was the money for the party fund collected in cash or through cheque? If it were through cheque to which account was it deposited? If it was through cash was it black money?" the BJP MLA asked in the letter to Kumar.
He also alleged that Kumar, the former Himachal Pradesh Chief Minister, was lying about the letter (written by Kumar to Shah) getting leaked on Facebook and Twitter.
"You want to put everyone on the dock and show yourself as an idealistic and honest person. But try to see yourself in the same light in which you want to project others," he said.
In his letter to Shah, Kumar also referred to allegations in some states, hinting to the controversy in Rajasthan surrounding CM Vasundhara Raje over the Lalit Modi controversy and Maharashtra where there are allegations of corruption against BJP minister Pankaja Munde.