The investigation, according to a timeline released by Kane, started in the last three months of then-Attorney General Tom Corbett's tenure in 2010.
Corbett resigned to take office as governor in January 2011 and was replaced by acting Attorney General Bill Ryan and then by acting Attorney General Linda Kelly.
Kane took office in January 2013.
"This criticism goes across the board to the attorneys general who started this to the current attorney general," Wolf said of Corbett and Kane. "If the investigation was proceeding down a bad path, put it on the right path."
Kane called the investigation "deeply flawed" and said that federal prosecutors and the Dauphin County District Attorney's Office, with jurisdiction in Harrisburg, concluded it could not be successfully prosecuted.
One of Kane's concerns is the decision made 45 days before she took office to drop 2,033 criminal counts against the lobbyist, Tyron B. Ali, who had been accused of stealing $430,000 from a state program meant for poor children and senior citizens.
Wolf, who said the elected officials who allegedly took money and gifts should be "held accountable," called Ali's deal a "get-out-of-jail-free card."
The other Democrats in the race, U.S. Rep. Allyson Schwartz, state Treasurer Rob McCord, former Environmental Protection Secretary Katie McGinty and former state Auditor General Jack Wagner, speaking at a candidate forum in Philadelphia on Sunday, all raised concerns about the investigation but declined to question Kane's judgment.
On Twitter: @ChrisBrennanDN