Usually NSA of FBI, if it is an international non American hacker CIA might get involved. IF a specific agency is targeted then that agency would usually get involved like if CID was targeted then they would most likely help investigate
What you should be asking is whether there is a hacker agency to protect you from Government.
The NTSB (National Transportation Safety Board).
Government agency of which country are you asking about. Please make your questions precise if you want us to answer them for you.
USA
a federal agency that investigates complaints of employment discrimination
The police
The Environmental Protection Agency, The Army Corps of Engineers and The Coast Guard. There are probably others depending on the situation.
The US Postal Inspection Service.
Question needs to be more specific. There are several federal law enforcement agencies that could be involved depending on the crime and the agency.
office of the special counsil
Dog the bounty hunter.
norad