Generally speaking, it is okay to be scratched by a domestic cat and cause slight bleeding without injection, because not all cats carry rabies virus. Domestic cats normally do not carry rabies virus, and rabies virus is spread through saliva and blood. Scratches are generally not contagious, so you don’t need injections. You just need to clean the wound in time and then disinfect it.
Tips:
If you are worried, you can observe the cat for seven days. After seven days, the cat will be fine if there is no abnormal reaction. If there is any abnormal reaction, get vaccinated immediately.