The 17-year-old joined Gary Megson's side on transfer deadline day after the north-west club agreed to pay a reported £1million fee for the player.
But Wolves allege that Connolly, capped by the Republic of Ireland at youth level, was subject to "unapproved communication" from Bolton assistant manager Chris Evans - a former academy chief at Wolves - prior to the deal being concluded and have now reported their concerns to the authorities.
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The newly promoted side's chief executive Jez Moxey said: "We have lodged an official letter of complaint, supported by considerable amounts of documentary evidence, with both the Premier League and the FA.
"This complaint relates to Bolton Wanderers and their assistant manager Chris Evans, a former Wolves employee. We allege that there has been a breach of the Premier League and FA rules in place to protect a club's academy programme, maintain player contract stability and prevent illegal approaches of players.
"It is not an issue about money or the level of compensation we received for a player we did not want to leave; it is about the protection of the club's academy programme and its development of young players, something which is of paramount importance to us at Wolves.
"We cannot sit on our hands and allow the events surrounding Mark Connolly's departure to pass unchallenged or unnoticed."
Evans joined Bolton from Wolves as assistant manager in November 2007 after 17 years in charge of youth development at Molineux. Bolton also signed another promising Wolves academy graduate, Mark Davies, in January.
Bolton have yet to be approached by the authorities about the case.
"We are aware of the statement issued by Wolverhampton Wanderers but we have had no official contact from the Premier League or the Football Association and have no comment to make," said a spokesman.