"The letter is basically a charge sheet against Hair outlining instances where we feel he violated the umpires Code of Conduct during the Oval incident," Saleem Altaf, director cricket operations, told Reuters on Tuesday.
The ICC have included the issue on the agenda of its executive board meeting in Mumbai on November 3.
After the fourth Test debacle against England at the Oval, where the hosts were awarded the match by forfeit after Pakistan refused to take the field amidst ball tampering allegations, Pakistan has refused to play further matches under the umpiring of Hair.
The England and Wales cricket board want Pakistan to pay over $1.5 million in compensation for forfeiting the Test.
Ranjan Madugalle, ICC adjudicator, cleared Pakistan captain Inzamam-ul-Haq of ball-tampering charges but banned him for four matches for bringing the game into disrepute at a hearing in late September in London.
The PCB claims that after the umpires had awarded the game to England, Hair refused to resume the match despite requests from ICC chief executive Malcolm Speed, the two boards and match referee Mike Procter.
The ICC had informed the PCB it would not launch an inquiry into Hair's conduct unless a formal complaint was filed highlighting instances where the umpire may have acted beyond his powers.
"We believe that an inquiry into Hair's conduct is necessary as it will have a bearing on the compensation claim filed by England against us for loss of revenues in the test," Altaf added.
"We also believe the forfeiture is a result and the match was completed."
Hair has insisted he acted according to the rules of the game and is not biased against Asian teams.
Hair, and fellow Oval fiasco umpire Billy Doctrove, were not included by the ICC on the umpires panel for the Champions Trophy in India.