Sorry, just saw this.
I think you mean private investigation that would otherwise be trespass? You could of course, preform an investigation at will to the extent that it did not infringe on anyone’s property rights (including their property of themselves).
It is entirely possible, and some people think probable or inevitable, that defense organizations would have their customers sign contracts that allow reasonable investigations. This is permissible under the NAP. Some innocent people might also prefer to allow the investigation or proffer evidence of their innocence, in this system where there are no victimless crimes and people are more or less reasonable.
What complicates this is that if you in fact committed the aggression, then the victim has retaliatory on you. And that includes using the retaliatory force of trespassing on your land to obtain evidence. So technically speaking, investigations are only a NAP violation if the one being investigated is innocent (or if they are preformed by a random third party with no assignment/trusteeship by the victim). This would leave the investigation agency in the position of not knowing if they were violating the NAP unless they had a contract or consent. This might lead to a more chaotic outcome than most people are willing to live with, so I imagine that most people in most circumstances would seek something like contracts or arbitration.
I can’t say exactly how it would work, and neither can anyone else, but I’m willing to bet that whatever people voluntarily agree to is immensely preferable to the system we have now where pseudo science is upheld by courts, rape kits sit on shelves for years, people get sentenced to life for weed, and people who have nothing to do with anything have their houses and cars torn up and the walls ripped out because someone who didn’t even put a name to their statement accused them of something that would be no one’s business even if it were true.
