A U.S. District Court judge yesterday set April 27 as the trial date for John W. Hinckley Jr., accused of attempting to assassinate President Reagan outside a Washington hotel more than a year ago.

The trial, which will focus on whether Hinckley was sane at the time of the shooting, had been delayed for months while government prosecutors appealed a court ruling barring them from using certain evidence in the case.

That issue was finally set aside this week when the full U.S. Court of Appeals here said it would not review Judge Barrington D. Parker's decision that the evidence had been obtained in violation of Hinckley's constitutional rights. When the Justice Department announced then that it would not seek further review of the matter in the U.S. Supreme Court, it cleared the way for Parker to set a trial date.

Hinckley's father, John W. Hinckley Sr., had criticized the Justice Department for "dragging its feet" in the case and said in a newspaper interview: "We've been ready to go to trial since November. . . ."

When Hinckley was arraigned on the charges last August, he waived his legal right under the federal speedy trial act to a trial within 80 days.

At a court hearing yesterday, the younger Hinckley's defense lawyer, Vincent J. Fuller, told Parker that he didn't think that any "inordinate delays" in the case had been caused by either the prosecution or the defense. Fuller then asked Parker to give the defense team 30 days to prepare the case for trial.

Assistant U.S. Attorney Roger M. Adelman opposed Fuller's suggestion. "We're ready for trial now," Adelman told Parker.

"I can't look kindly on your request for a 30-day delay of the trial," Parker told Fuller. Late yesterday afternoon, Parker set the April 27 trial date, one week short of Fuller's proposal.

At the hearing yesterday, Fuller told Parker that the defense expects to call four psychiatric expert witnesses and six to eight other witnesses to testify about Hinckley's mental state. The "longest and most extensive" testimony, Fuller said, will come from Hinckley's family.

Fuller also said at the hearing that he expects testimony at the trial from medical doctors who had treated Hinckley.

Hinckley has admitted in court papers that he fired the shots that injured Reagan, White House Press Secretary James Brady, a U.S. Secret Service officer and a District police officer. He has pleaded not guilty by reason of insanity.

The government plans to open its case with videotaped evidence and eyewitness testimony about the shooting, as well as evidence about Hinckley's activities in the months before the attack. Prosecutors contend that this evidence will prove Hinckley's actions were premeditated and will counter defense claims that Hinckley was insane at the time.

It is expected that the trial will begin with the government's presentation of the facts about the shooting. It is not known whether Reagan or any other of the victims will testify.