SWAT team members found the suspect, Evan Dorsey, 25, dead inside the trailer immediately after the incident early Sunday, state police spokesman Sgt. John Perrine said.
Howard County Sheriff's Department Deputy Carl A. Koontz, 27, and Sgt. Jordan J. Buckley, 35, were shot while trying to serve Dorsey with a warrant for failure to appear in court on charges of illegally possessing a syringe.
They entered the trailer after receiving no answer to a knock on the door, authorities said. Dorsey shot himself in the head, according to Howard County Coroner Jay Price.
Koontz, who had close to three years on the job, died from his injuries. An autopsy was scheduled for Monday.
Buckley, who was recently promoted to sergeant after nine years with the Howard County Sheriff's Department, was shot in the upper thigh but is expected to make a full recovery, state police Perrine said.
No one else was injured, Perrine said.
Buckley was released from Methodist Hospital in Indianapolis on Monday afternoon, in time to participate in a procession taking Koontz's body back to Kokomo. Dozens of vehicles from other law enforcement agencies also took part.
Indiana Gov. Mike Pence ordered flags to be flown at half-staff until sunset on the day of Koontz's funeral.
"Indiana will always honor the memory of Deputy Koontz and will always be grateful for his courageous service. Deputy Koontz lost his life in the line of duty, and his passing reminds us all of the courage and risk that every member of our law enforcement community and their families face every day in the defending our communities," the governor said in a statement.
"We also offer our gratitude and prayers to Sgt. Jordan Buckley, who was injured during the same incident in the line of duty. We are grateful for his courage and pray that he will make a quick recovery from his injuries and be restored soon to his family and his service to the people of Howard County."
Dorsey, the suspect, had a criminal history that included possession of a controlled substance, according to public records.