Formula One's governing body has ruled out any further action against BAR, who return after a two-race suspension at Sunday's European Grand Prix.
Jenson Button came in third at Imola
"The FIA regards the San Marino Grand Prix incident as closed," the International Automobile Federation (FIA) said in a statement.
"BAR are no longer under investigation, and the FIA wishes them every success."
BAR were punished when Jenson Button's car proved to be underweight after the Imola race.
The FIA then said it was investigating claims that BAR had brought the sport into disrepute with comments made by management about the suspension.
With BAR already under the threat of a six-month ban, suspended for a year, referral to the FIA's world motorsport council could have had serious implications.
BAR moved swiftly to stave off further action by accepting they had misinterpreted the regulations and accepting punishment.
Button finished third at Imola, but his car was found to be too light when fully drained of petrol hidden in a collector tank inside the main fuel reservoir.
Both he and team-mate Takuma Sato were stripped of their points, the team's first of the year.