Slight bleeding from a scratch by a pet cat generally does not require an injection, but the wound needs to be washed with soapy water for more than 15 minutes, then the blood in the wound is squeezed out, and then iodophor is applied for disinfection. Pet cats generally do not carry rabies virus, and rabies virus is usually transmitted through bites, so they are basically not infected with rabies.
Tip:
If you are scratched by a stray or feral cat, it is best to go to the hospital for vaccination.