SANTA MONICA, Jan. 3 – The father of slain actress Sharon Tate was appointed administrator of her estate, estimated at $45,000, in a petition approved in Santa Monica Superior Court Friday.

In the petition, Miss Tate’s father, Paul Tate, 47, of Palos Verdes, said his daughter did not leave a will. He listed her assets as $37,200 cash, $5,700 in automobiles, $2,000 estimated annual income and $500 other personal property.

The estate would be shared with the actress’ husband, Roman Polanski, Miss Tate’s mother, Doris, 46, and the actress’ sisters, Deborah Ann, 17, and Patricia Gaye, 12, Tate said.

He did not specify how much each would receive.

Miss Tate, 26, was slain Aug. 9 with four other persons in her Bel Air home. The County Grand Jury has indicted five persons in connection with the deaths.