Miller was arrested Monday night at LaGuardia Airport in Queens, New York.
The 36-year-old actor is accused of "intentionally transmitting false information about an explosive device to the police."
Appeared before US District Judge Jeffrey A. Meyer in New Haven, Connecticut on Tuesday and was released with a $ 100,000 bonus.
The charge carries a maximum sentence of five years in prison.
According to a Justice Department press release, Miller called a 911 dispatcher in New Jersey on March 18 and reported that he was on the 2256 Amtrak train that was traveling from Washington, DC, to Penn Station in the city of New York with a passenger who, he said, had a "bomb in his bag."
Amtrak officials stopped Train 2256 at the Green & # 39; s Farms station in Westport, Connecticut. The passengers were told to stop before the members of the bomb squad got on board and searched the train.
No evidence of any explosive device or material was detected, officials said.
An investigator called Miller back, according to the Justice Department press release, and gave him a different description of the woman.
Miller is alleged to have also asserted that the woman "continued to check her purse without removing anything, kept asking the first-class employee what was the next stop, and seemed to want to get off the train and leave her purse".
Miller was discovered to actually be traveling on the 2258 Amtrak train, not 2256, and that the train was also registered and had no explosive device, according to authorities.
DOJ officials added that Amtrak officials interviewed a first-class car attendant, where the actor had been sitting, and told them that Miller appeared to be intoxicated and had been involved "in hostile exchanges with a woman who was sitting in a row different from yours in the first class car. "
Miller came out "Silicon Va Lley" amid the creative differences with the showrunners last year.
CNN has contacted the actor's representatives to comment.
Gabriela Milian from CNN contributed to this story.