When my dad ctb the detectives showed up, got everyone's stories about how finding him played out, and mostly milled about until the coroner showed up to confirm the death. The body was then taken and the detectives left. They took his PC because there was no note and they wanted to see what they could find, also took the gun (we had to fight to get the pc back, never got the gun back, no follow up on anything found)
When my ex ctb/overdosed, it was more or less the same, only we still thought he could be saved so paramedics showed up, attempted resuscitation on site, eventually took him to the hospital for further attempts but he was pronounced dead. The detectives/cops stayed at the house after he was rushed off, I stayed with them, I got the call from his mom and told them he had passed. They questioned me same way as with my dad, asked me if there were any other drugs in the house. They took his phone (which I also never got back, also no follow up about anything) and that's about it.