Calvert was discovered unresponsive Saturday afternoon on the band's tour bus, which was parked outside a club where the group was slated to play that night, said an ABC news affiliate in Washington.
Help was called, however, Calvert was pronounced dead at the scene, the report said.
"Casey Calvert passed away in his sleep last night. ... At this time we're not sure what exactly happened. Just last night he was joking around with everyone before he went to bed," the band wrote on its Web site Saturday.
"We can say with absolute certainty that he was not doing anything illegal. Please, out of respect to Casey and his family, don't contribute or succumb to any gossip you may hear. We don't want his memory to be tainted in the least. Casey was our best friend. He was quirky and awesome and there will truly be no others like him. His loss is unexplainable. As soon as we know more we will let you know."
The Ohio band began a 28-date U.S. tour in Detroit Friday, the Dayton (Ohio) Daily News reported Monday.