The company's lawyers told a judge they need the money to cover the costs of preserving evidence, retrieving and copying records, travel and other expenses, according to court documents filed this month.
A judge didn't immediately rule on the request. But Colorado courts allow the winning side of a court case to recover legal fees.
Jurors in May ruled in Cinemark's favor over 28 victims and their families who argued the nation's third-largest theater chain should have done more to prevent the attack that killed 12 people and left more than 70 others injured. They sued in state court, saying security lapses allowed for the July 20, 2012 attack at a midnight premiere of a Batman film.
A judge last week dismissed a similar lawsuit in federal court, saying Cinemark's lack of security was not a substantial factor in the deaths.
In both lawsuits, victims cited a lack of guards and no alarm, including a silent alarm, on an emergency exit door that would have sounded when James Holmes slipped into the crowded theater and started shooting.
The company argued that no security measures would have predicted or stopped the armor-clad Holmes. After months of meticulous planning, he threw gas canisters into the crowd of more than 400 and then opened fire with a shotgun, assault rifle and semi-automatic pistol.
Cinemark argued it could not have foreseen the attack. Lawyers for the plaintiffs in the state case have said they are considering appealing the verdict.
If Cinemark had lost the case, it could have forced theater companies across the U.S. to adopt costly security measures that could have increased ticket prices significantly, experts said.
Holmes is serving a life sentence after a different group of jurors could not unanimously agree on whether he deserved to die.