Sometimes you hear about an investigation involving you from someone else. Maybe a former business partner had a knock on her door from someone associated with the police. Maybe a former co-worker heard about someone being given a grand jury subpoena for testimony. If you hear about an investigation involving you from someone else, you may have the luxury of advance notice.
As well, if you have friends or relatives who are close to you they’ll let you know. This is because usually, at some point, the police will contact them and, despite their being instructed NOT to alert you, they are going to do so anyway. They likely will tell you for a variety of reasons. They may be concerned about you, they may think that they get some money from you for it, or they may simply not like the police. Whatever the reason, it is highly likely that within a short time span after the police contact them, they are going to contact you and you’ll know that something is going on.
Additionally, if people who you have known for a long time (but are not close to) are beginning to treat you differently (not as talkative, not wanting to be around you too often, looking nervous when you approach, etc.) then it’s likely that they are concealing something. Unless something else is going on in your life that may involve such secrecy (possible spousal cheating, etc.), then it’s possible that they have been contacted by the police seeking information.
Another way to know is the obvious way. You will most certainly know when the police choose to contact you directly – for a “knock and talk”, to interview you and/or to arrest you. Even though it is seldom wise to reveal to the subject of that investigation what is brewing until all those needed to be interviewed have been.
Please note that the police are under no obligation to tell or admit that you are under investigation. This applies only to open, ongoing investigations. Closed investigations fall under FOIA and must be revealed if push comes to shove.