It depends. I think any death outside of the hospital, at least one without an obvious natural cause, requires the police to get involved. The coroner determines the cause of death. If evidence points to suicide, they'll need to determine if anyone else was involved. Maybe someone encouraged you to do it, or maybe someone threatened or bullied you. Maybe someone provided you with the resources to kill yourself knowing what you're up to. I don't know how thoroughly they'll investigate each of these options. They'll probably start with family, friends, coworkers/classmates, neighbors. Also they'll probably check your phone records, they'll try your devices too. Unless they get enough answers before that. Keep in mind they don't care enough to investigate all your life. Once they get enough to close the case, they don't bother.
They need to know:
1. Why did you kill yourself
2. How did you kill yourself
3. Where did you get the idea from? (method)
4. How did you obtain the means to do it? If illegally, they might want to pursue it further.
5. Did anyone help you? (either by assisting, advising or providing you with the means while knowing your intentions)
How deep do they need to dig to tick all these boxes? You tell me. When I was attempting to CTB I left a QR code in a visible place with a link to a video in which I answered all these questions in detail, so that they would close the case quickly and leave my family alone. I don't know if it would've worked, but I thought it might be worth a shot.