The half-brother of Saudi Arabia's King Khalid has been granted diplomatic immunity by the State Department more than a month after he was accused of assaulting Miami police officers.

Prince Turki bin Abdul Aziz is one of the 43 sons of the founder of the Saudi royal family and is closely related to many senior Saudi officials, but he holds no position in the Saudi government at this time.

The State Department, in response to inquiries from reporters, said yesterday that it had granted diplomatic immunity to the prince and his wife, Princess Hend al-Fassi, April 1 in accordance with a request from the Saudi king. Department spokesmen declined to describe the prince's position or mission here.

The prince was a deputy Saudi defense minister until 1978 when, according to a new book, "The House of Saud" by David Holden and Richard Johns, he fell from grace because of a marriage that the royal family did not regard highly and perhaps a "partiality to alcohol."

According to news agency accounts yesterday, which identified the prince but not his relationship within the Saudi family, the case has stirred considerable anger among police and prosecutors in Miami. Five officers allegedly were assaulted Feb. 26 while investigating allegations that the couple were holding servants as slaves at their quarters in a luxurious condominium.

No such servants were found, the Associated Press reported yesterday, but several Miami police officers, including one who said her hand was smashed in the door of the apartment, have filed civil damage suits against the couple.

"I can't believe that in this country a person can buy immunity from the law," Connie L. Kubik, one of the officers involved who has resigned, told the Miami Herald this week.

The Saudis, in turn, have filed suits for $210 million in damages, claiming that the police were "abusive, disgusting and violent."

On March 19, two State Department officials were dispatched to Miami. According to the department, they "were asked to express to Prince Turki the concern of the department over the situation in which he was involved and its implications for Saudi-U.S. relations, its appreciation of his position within the Saudi royal family and its desire to assist in resolving the situation in every appropriate way."

As long as the couple hold diplomatic immunity, they cannot be prosecuted. A spokesman for the local police department in Florida was quoted yesterday as saying that while officials there believed they had "a good case," they were aware of the international implications and do not plan to prosecute at this time.