Conductor Julius Rudel will sever his connection with the New York City Opera, effective in mid-December, after 35 years of association with the company, including 22 as its general director. His decision was announced yesterday in a joint statement by Rudel and Beverly Sills, who succeeded him as general director last year.

Rudel said that Sills, who has been his associate for many years, accepted his request for a release from his contract reluctantly but in "a spirit of deep-seated friendship."

In asking for the release, Rudel reminded Sills that "some years ago, I did you the favor of releasing you from several performances at the City Opera so that you could make you La Scala debut. Now, I would like to ask you for a similar favor -- to release me from all future commitments after the end of the 1980 fall season."

Sills said she was "heartbroken" at Rudel's decision but would not hold Rudel to his contract against his will. Unlike his release for her La Scala debut, when "he knew I would be coming back," she said, Rudel's request left prospects of "no coming back in the immediate future."

"The company will miss him," she said, "the public will miss him, and . . . most of all, I will miss him."

Rudel's severance from the City Opera has been considered inevitable since he was removed from the general directorship -- reportedly in an atmosphere of considerable bitterness -- but the timing of his decision came as a surprise.

The official reason given for the severance was the pressure of other commitments, and there are certainly enough of them to make this seem plausible. Besides being the conductor of the Buffalo Philharmonic and a guest conductor with many other orchestras, Rudel has operatic conducting assignments in Vienna, Hamburg, Prague, San Francisco and Buenos Aires and at the Metropolitan in New York. He is also about to begin a long-term association with the Chicago Lyric Opera on terms that have yet to be worked out. Earlier, Rudel was the Kennedy Center's first musical adviser. w

Sills and Rudel both agreed that, in spite of his severance from the company, he will conduct her gala farewell performance at the City Opera next October.