The boy was rushed to a private hospital, police sources said.
The incident happened this evening at Neelangarai Police Station where the inspector (crime) was questioning the boy, they said.
"The incident happened accidentally. The boy is alive," Joint Commissioner (South) Thirugnanam told PTI when inquired about the boy's condition.
Details of the accused and the inspector were immediately not known.
The accused is said to be in a critical condition in the private hospital, where he is being treated for bullet injuries.