President-elect Joe Biden now leads President Donald Trump by more than 7 million votes in the 2020 election.
The petition alleged Wisconsin election officials were directed to fill in missing information on ballot envelopes, issued absentee ballots without receiving applications and allowed people to improperly claim a "confined" absentee voting status.
Mr Trump has refused to concede the election and has repeatedly continued to pursue unsuccessful court challenges.
Mr Trump hasn't yet said whether he will be attending the inaugural event or not but according to a report published by NBC News on Wednesday, he is planning to skip it and will not even invite Mr Biden and his wife Dr Jill Biden to visit the White House beforehand, as is the custom.
Another legal blow came Thursday, the day after Trump posted a 46-minute speech to Facebook filled with conspiracies, misstatements and vows to keep up his fight to subvert the election.
The fine print made clear most of the money would go to other priorities, including retiring the debts of Trump's campaign.
Failing to gain any traction in court, Trump and his allies are now turning to events with Republican lawmakers and rallies in states like Pennsylvania, Georgia and MI where they can use unfounded claims of fraud to incite the president's loyal base. They've also been quite lucrative, however.
That will be a boon to the Republican National Committee, as it seeks to retire any debt incurred over the campaign.
Kelly's lawyer Greg Teufel, who specializes in breach of contract disputes, did not immediately return an email requesting comment.
In the state's courts, justices cited the law's 180-day time limit on filing legal challenges to its provisions, as well as the staggering demand that an entire election be overturned retroactively.
"To date, we have not seen fraud on a scale that could have effected a different outcome in the election", he said.
US President Donald Trump has urged members of the Republican Party to "get tough". Mr Biden also leads the popular vote by almost seven million ballots.
Hearings on both lawsuits were scheduled for Thursday, with the judges noting the importance of resolving the legal battles before the Electoral College meets on December 14.
Mr Biden is due to be sworn in on 20 January.