Tony Owens, the attorney representing the alleged victim in a civil lawsuit, said his client is disappointed.
"The victim feels victimized again by the system. But it doesn't affect the civil case," Owens told the newspaper.
The Associated Press does not identify sexual assault victims. A Tarrant County grand jury indicted Carter, 51, in June after a licensed minister at a Dallas CME church said Carter in March 2007 tried to force him to have sex when the man applied for a job.
A month after the indictment, the Christian Methodist Episcopal's College of Bishops said it was suspending Carter with pay until his criminal case was resolved.
Brian Salvant, the attorney representing Carter, had said in a previous civil court appearance that the accuser had been a "full participant" in a relationship with Carter.
Salvant said Carter had cooperated with the police and prosecutors including passing two polygraph tests. Carter admitted to having a consensual sexual encounter with the man, in depositions.
Before being elected bishop in 2006, Carter served 10 years as pastor at the Carter Metropolitan CME Church in Fort Worth.
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