The former Bolingbrook police officer is also charged in criminal court with murdering Savio.
Peterson's attorney had asked that the judge issue a stay on the Savio family's civil case pending the outcome of the criminal case.
"The judge didn't stay the case, didn't freeze the case. But he also said that Drew or indicated that Drew can take his Fifth Amendment privilege in answer to any question or any pleading," said Joel Brodsky, Peterson's attorney.
Savio's death was originally ruled an accident, but the case was determined to be a homicide after Peterson's fourth wife Stacy disappeared.