"The situation escalated, for reasons under investigation, and resulted in at least one officer firing his service weapon, striking Cummins", TBI spokesman Josh DeVine said.
On Sunday, the TBI said in a statement the body of two more victims had been found at the home.
They believe Cummins may be in the woods in the area near one of the homes. A fifth, injured victim was also at the home, and transported to the hospital.
Weatherford said the bodies were found inside a house on Harve Brown Road between Portland and Westmoreland in a suburb, northeast of Nashville.
Authorities did not say how they were killed or whether or how the victims were related to each other. DeVine said it's possible that there is a sixth victim hospitalized.
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A family friend identified three of the deceased victims as relatives of Cummins: David and Clara Cummins, the mother and father of the suspect, as well as Charlie Hosale, Cummins' uncle.
Police in Sumner County, Tennessee were looking for a suspect on Saturday evening believed to be responsible for the deaths of five people.
Police vehicles on Sunday blocked access to roads outside the homes.
On Saturday night, the helicopter found indications of an individual in a creek bed about 1 mile (1.6 kilometer) from the first scene, after which a SWAT team was sent to the location. No officers were injured. Cummins is being treated at a local hospital for what's believed to be non-life-threatening injuries, DeVine said.
The shooting of Cummins remains under investigation, according to the TBI.