The suspect carjacked a vehicle after the traffic stop near Lexington's airport and fled to Richmond Road Baptist Church, where he opened fire, Lexington Police Chief Lawrence Weathers said on Sunday.
Killed in the shootings at the church were a 72-year-old woman and a 32-year-old woman.
Two other people were wounded at the church and taken to a local hospital, the police chief said.
One victim has critical injuries and the other is in a stable condition.
The suspect was shot by police and died at the scene, he said.
"Preliminary information indicates that the suspect may have had a connection to the individuals at the church," the police chief said at a news conference.
The trooper stopped the vehicle after receiving a "licence plate reader alert" and was shot about 11:30am, Weathers said. The trooper was in stable condition, he said.
Police tracked the carjacked vehicle to the Baptist church, about 26km from where the trooper was shot, the police chief said.
Fayette County Coroner Gary Ginn said the church was home to a small, tight-knit congregation.
"Please pray for everyone affected by these senseless acts of violence, and let's give thanks for the swift response by the Lexington Police Department and Kentucky State Police," Kentucky Governor Andy Beshear said in a social media post.
State Attorney General Russell Coleman said detectives with his office were ready to support local and state agencies.
"Today, violence invaded the Lord's House," Coleman said in a statement.
"The attack on law enforcement and people of faith in Lexington shocked the entire Commonwealth."
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