ALBANY – The estate of a businessman held to be responsible for taxes on a once-prosperous Manhattan strip club does not have to pay more than $4 million in back taxes because the club became so thoroughly infested by organized crime that it was unmanageable, a state administrative law judge has determined.

While the late Frank A. Marchello was properly held by the New York State Department of Taxation and Finance as being a responsible officer for the V.I.P. Club, Administrative Law Judge Winifred M. Maloney concluded that Mr. Marchello was thwarted, through no fault of his own, in carrying out his corporate duties by mob influence that one federal prosecutor said had “bled the club dry” financially.