The incident occurred when Jayson Castaneda, 24, was leaving the county courthouse Friday afternoon. Neither deputy was seriously injured.
Castaneda was in court on a charge of failing to appear at a previous court date. He ran from the courthouse after finding out there was a warrant out for his arrest.
Castaneda was captured at a residence in Morristown on Sunday.
"He was hiding in a closet," said Officer David Cribley of the Hamblen County Sheriff's Department.
According to authorities, Deputy Bob Schaff was sideswiped outside the courtroom when he ran after Castaneda. Deputy Craig Cloer tried to stop Castaneda by stepping out in front of his car.