The girls and their parents say the order by Cuyahoga Juvenile Court Judge Alison Floyd questions the victims' honesty. None of the girls complied.
The judge also ordered the four teenage boys accused of rape and other sex crimes in the cases to undergo polygraph tests as part of an assessment before sentencing. Floyd found them delinquent, the juvenile court equivalent of guilty.
The Plain Dealer newspaper said the judge's intent is unclear and she hadn't responded to requests for comment. A message was left Friday at her office by The Associated Press.
"The situation made no sense to us," the mother of a 16-year-old victim told the newspaper in a message relayed through the Cleveland Rape Crisis Center.
The mother said her daughter's attacker told people that the polygraph requirement showed the judge didn't believe the girl's accusations.
Terri Stupica, an attorney representing one of the boys, said Friday that the judge proposed the polygraph requirement for the victim, not the defense. She declined further comment.
Prosecutor Bill Mason's office has filed briefs in two cases, asking the judge to stop ordering rape victims to submit to polygraph tests, and said Friday a challenge would be filed in a third case that it has identified.
The judge does not have authority over victims, according to the motion filed by assistant Prosecutor Nicole Ellis.
"Ordering a victim to submit to a polygraph test is harassment and is being done to punish the victim and is not necessary to rehabilitate (the) delinquent," the prosecution said in challenging a polygraph test for a victim in a case from last June 18 in suburban Brecksville.
The victim said she was fondled and forced to perform a sex act. The boy admitted to three counts of gross sexual imposition.
The polygraph requirement violates the spirit of Ohio's rape shield statute designed to protect victims of sexual assault, the motion by prosecutors said.
Megan O'Bryan, president and CEO of the Rape Crisis Center, said the center - which is assisting three of the victims - does not condone the polygraph tests for sexual-assault victims.