The injured trio, identified as Jai Kumar, Sunil and Dinesh from Bantla police post, met with the accident during patrolling last night, police said.
They were admitted to a nearby hospital where the condition of Kumar and Dinesh is said to be critical.
The car sped off after the incident, a senior police officer said.
"We are scanning CCTV footage of cameras installed nearby to identify the car's registration number," he added.
"A case has been registered and we will record the constables' statement once they recover," he said.
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