Can a civilian legally investigate a crime and take down criminals on his own?

I do not know what country the guy previous to me is from, but you do not need to be a cop to make an arrest. You have the right to make a citizens arrest if there is evidence as sufficient as a member of law enforcement would need to make an arrest. Use of force must be equal to the person you are detaining... for instance if they punch you you cannot shoot them. However if your life is in danger you can shoot them. I suggest not investigating crimes as you may cross a line without being an expert on law. It is easy to slip and do something that incriminates yourself whilst trying to do the right thing.