The widow and daughters of the dead weapon expert had asked government lawyers on whose authority, anonymous leaks were being made to the press, including comments that described Kelly as a "Walter Mitty" character.
The six-page fax that the family sent was among the 9000 pages of documents released on Saturday by the independent judicial probe into Kelly's death.
At the centre of a row over whether the government had exaggerated Iraq's weapons of mass destruction, Kelly reportedly committed suicide by slashing his own wrists, soon after he was named as the source for a story on the BBC.
Apart from being described as a fictitious compulsive fantasist, anonymous government sources alleged the expert was being investigated for repeated unauthorised leaks to the press.
But the smear campaign hurt his family and their lawyer shot off a strong note to the government.
"If information of this nature is being disseminated, either formally or informally, I should like to know on whose authority this is being done," family lawyer Peter Jacobsen asked.
"On the one hand the government for every good reason is calling for restraint during the course of the inquiry which has, of course, commenced. On the other hand the various arms of government appear at least through the press to be following a different course," the fax said.
"Kelly has now been the subject of criticism in the media without the facts having been first established," Jacobson added.
Three days before the fax was sent, one of Prime Minister Tony Blair's official spokesman had apologised to the family for lampooning the dead expert.