White House press secretary James S. Brady, who was shot in the head during the attempted assassination of President Ronald Reagan last March, filed a $46 million civil suit against John W. Hinckley Jr. yesterday in U.S. District Court here.

Hinckley has admitted firing the shots that also injured Reagan, a District policeman and a Secret Service agent.

Brady, 41, was the most seriously injured of the four victims in the shooting outside the Washington Hilton. He spent eight months in George Washington University Hospital, leaving there last November still unable to walk without crutches and with his left arm still paralyzed.

In the lawsuit filed by Brady's attorney, Jacob A. Stein, Brady sued Hinckley for assault causing "severe and permanent injury," asking for $8 million in compensatory damages and $15 million in punitive damages. He also sued Hinckley for negligence, asking $8 million in damages, and for acting "willfully, wantonly and with a reckless disregard for human life," asking for an additional $15 million in damages on that count.

Brady is the second victim to sue Hinckley. Thomas K. Delahanty, the former District policeman who was struck in the shoulder and neck by a bullet fired by Hinckley, sued him last month for $12 million in damages.

Hinckley said in court after his arrest that he had no property or bank accounts, and he was found to be indigent by a U.S. magistrate. Hinckley's family retained lawyers from the local firm of Williams & Connolly, who are representing him both on the criminal charges and in the civil suit.

Delahanty's lawyer, Robert Cadeaux, has said that he believed Hinckley "may be covered by an insurance policy either under his own name or within the family" that could include coverage for negligence. Cadeaux said he also believes there may be a trust fund in Hinckley's name that could be tapped if Delahanty were to win his suit.

Hinckley's brother Scott, reached yesterday at the family-controlled Vanderbilt Energy Co. in Denver, said he was not aware the suit had been filed and could not discuss either the family's finances or their response to the legal action.

"That information is personal and our lawyers have asked us not to discuss the financial condition of my brother or the family," Scott Hinckley said.

Hinckley's lawyers have asked that the civil cases be put off until the conclusion of the criminal trial. Cadeaux said he has filed a motion asking to proceed with some pretrial matters, but he acknowledged yesterday that the civil trials probably would "be put on the back burners" until the criminal trial is over.