A Maryland State Police trooper and an Eastern Shore man who had called the state police for help were both shot and fatally wounded yesterday in the Brookview area of Dorchester County, authorities reported.

The slain trooper was identified as William P. Mills, 32, a nine-year veteran of the state police who was assigned to the Easton Barracks.

The other victim was identified as Myron W. Thomas, 31, of the rural Brookview area, about five miles west of the Maryland-Delaware border.

State police said Richard H. Bassett, a neighbor of Thomas, was arrested at the scene and charged with two counts of murder.

According to the state police, Thomas called yesterday to complain about a possible assault or threat of an asault and Mills was sent about 4:30 p.m. to investigate.

Shortly after leaving his patrol car, Mills was struck by one or more shots in the chest, police said. It was not immediatly known when Thomas was shot. Police said he was struck in the body.

A resident of the area called for help on the radio in Mills' car, and troopers who responded placed Bassett under arrest, police said.

Thomas was pronounced dead at the scene. A state police helicopter took Mills to Peninsula General Hospital in Salisbury at 5:45 p.m. He was pronounced dead about five minutes later.

"We worked on him, but there wasn't much we could do," a hospital spokeswoman said.

Mills was married and the father of two children, police said. He was apparently the first trooper killed while on duty since December 1977, when a 27-year-old trooper was fatally wounded in Anne Arundel County after making a routine traffic stop.

Police said the suspect was being held last night without bond in the Dorchester County jail in Cambridge. CAPTION: Picture, WILLIAM P. MILLS . . . shot in the chest