A former Superior Court judge who won a multimillion-dollar libel suit against the Boston Herald does not qualify for a disability pension because he could not prove that he was handling judicial tasks when he received a written death threat, the state’s highest court ruled Friday.

In a unanimous ruling, the Supreme Judicial Court said Ernest B. Murphy was properly denied a disability pension by the state’s Contributory Retirement Appeal Board.

Writing for the SJC, Justice Francis X. Spina said that under state retirement law and earlier SJC rulings, Murphy had a legal burden to prove that he was performing some task related to his job as a judge when he read the death threat.

“Judge Murphy has not presented any evidence to support a conclusion that he sustained a personal injury during the performance of his judicial duties,’’ Spina wrote.

An attorney for Murphy did not immediately respond Friday evening to a request for comment.

According to the SJC, Murphy was appointed to the court in 2000 and became the subject of coverage by Boston Herald reporter Dave Wedge that was “sharply critical of Judge Murphy’s performance of his judicial duties.’’

Murphy, according to the SJC, subsequently received hate mail, death threats, and “threats of violence directed at his family’’ and received protection from State Police, notably after a copy of the Herald containing his photograph was slipped under the door of his judicial office with a bullet hole drawn on his forehead.

Murphy was diagnosed by his psychiatrist with post-traumatic stress disorder and major depression as a result, and was diagnosed by other doctors as having a variety of physical ailments.

He sued the Herald for libel and won a $2 million judgment, which climbed to $3.4 million with interest when it was paid by the newspaper.

Murphy was sanctioned by the Commission on Judicial Conduct for sending a letter on court stationery to Herald publisher Patrick Purcell seeking to settle the case before appeals.

In 2007, Murphy sought a disability pension, but was eventually denied the pension by the Contributory Retirement Appeal Board because it concluded that while the Herald articles and the death threat contributed to his poor mental and physical conditions, they were not the “proximate cause” of his disabled condition.

On Friday, the SJC sided with the retirement board and against Murphy.

“We examine the evidence from two perspectives — whether Judge Murphy was engaged in judicial work (such as preparing for a trial, doing legal research, or the like) during the time that he opened and read the death threat, and whether the act of opening and reading his mail was, in itself, a judicial duty,’’ Spina wrote.

In this instance, the SJC said, Murphy failed to prove his claim.

“It was incumbent on Judge Murphy to present evidence to show that at the time he sustained his personal injury, he was engaged ‘in the performance of’ his judicial duties’’ under state law. “He simply did not satisfy this burden of proof.’’