You are a suspect in a crime -- did you commit one? What is the due process in investigating? The investigator can't ask questions of neighbors, co-workers etc.? Stake out a home or business? All that is invading privacy, and you're still considered an innocent person.
Why are you asking me questions that are already answered in our law? Due process and the limits on our government in investigating crimes are laid out in the Constitution, and examination of other laws clarifying these things should answer your question.