The incident occurred in Sadar police station area when accused Gheesu Singh entered the room of his 21-year-old daughter Asha Kanwar and shot her dead while she was lying on her bed.
Moments later, he went to his room and shot himself with the gun, SP Chittorgarh Prasanna Kumar told PTI.
The SP said that the reasons behind the murder and suicide were not clear yet.
"The matter is being probed to ascertain the causes. The bodies were handed over to family members after post-mortem," he said.