A trial in the case was scheduled to begin Dec. 11 in county Common Pleas Court.
The indictment alleged the woman was impaired because of a mental or physical condition and the alleged perpetrators knew of that impairment.
Covault posted bail of $200,000 the day of arraignment while Perkins remained jailed on the same amount. He faces other charges in a separate incident, but his release on a recognizance bond with conditions was approved Wednesday morning by Judge Christopher Gee.
The dismissal was without prejudice, meaning another case could be filed in the future.
"I can't try a case without a victim on board," said Miami County Prosecutor Anthony E. Kendell.
Whether a new case would be filed depends on the accuser, he said.
Covault worked as a Troy firefighter/paramedic from May 1996 until retirement April 1, according to city personnel records.
Those records show he reported to Fire Chief Matthew Simmons on March 2 that he was under investigation for alleged misconduct earlier that day. He was placed on paid administrative leave that day and then on unpaid suspension March 5 pending completion of the city investigation into the alleged misconduct.
Covault notified the chief of his retirement March 15.
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