Jones had to spend the night in jail while waiting for a blood test, which could not be taken until Wednesday morning. He will appear before a grand jury on Jan. 13.
"I'll let everything play out in court," Jones told reporters after being released Wednesday. "Obviously, without getting into it, none of this makes sense."
Jones demonstrated lightly poking someone on the arm.
"For touching a guy, like this, I got arrested," Jones said. "We'll see how it goes. I'm more than [confident] that this will be dismissed pretty soon."
Jones also apologized to Bengals fans and said he would likely meet with coach Marvin Lewis and discuss what happened soon.
"I'm sorry that this happened. It would be different if I was beating people's ass, but for touching someone?"
Jones shook his head and walked away.
Jones, 33, was arrested at a hotel near the Bengals' stadium and the city's entertainment district in downtown Cincinnati and booked in the jail at approximately 12:30 a.m. Tuesday
When arrested, Jones refused to enter the police car and allegedly pulled away before kicking and head-butting an officer, jail documents said. He then spit on the hand of a nurse while he was being booked into the Hamilton County Justice Center.
"Obviously the events of last evening are not something that you want to have happen," Lewis told the Cincinnati Enquirer on Tuesday night during a live internet show. "Unfortunately it did. Our people are investigating that. You don't want charges against any of your people. ... Our people will investigate, our security as well as the law enforcement here locally, and it will play out, and everything will kind of go from there."
"Adam came here from about a low as you could get and we gave him an opportunity, and he has done well with that opportunity. This latest thing will have to play out."