The United States has protested to Yugoslavia the arrest of a young American by Serbian police in troubled Kosovo Province, the State Department said yesterday.

Shaban Kastrati, 19, of Plainfield, Ill., was arrested at a checkpoint in Pristina, the capital of Kosovo, on Aug. 29 as he was driving home with two friends after going to the capital to welcome a U.S. congressional delegation led by Senate Minority Leader Robert Dole (R-Kan.)

His father, Mike Kastrati, who had taken his American-born son to Kosovo in July and left him there with his grandparents, said Serbian security officials asked the youth and his friends to produce identification. When young Kastrati showed his U.S. passport, the father said, the police "grabbed him and beat him up." A U.S. consular officer from Belgrade who visited Kastrati in a Pristina prison on Monday said the youth had a cut chin and lip and "bruises all over his body," the father said yesterday.

The State Department said young Kastrati was charged with participating in a demonstration and throwing rocks at police officials and was sentenced on Aug. 31 to a 60-day prison term. A formal protest was filed with the Yugoslav Foreign Ministry on the basis of the youth's account and the consular officer's observations, a State Department official said.

Dole and Sen. Alfonse D'Amato (R-N.Y.) cabled the U.S. ambassador to Yugoslavia, Warren Zimmerman, urging the Belgrade embassy to secure Kastrati's release. In a statement yesterday, Dole said he was "doubly disturbed that the arrest took place in the context of our visit to Kosovo, when police of the ruling Serbian minority brutally broke up peaceful crowds {of ethnic Albanians} who had come to see us and express their concerns."

The older Kastrati, who had planned to open a family store in Kosovo, said he found his son's arrest "unbelievable."