In what way- cooperate with them? I guess it depends on them and you partly. Whether they bother to search your devices and, how thoroughly. Whether you leave pages open, search histories present, logins active. How easy you make it for them.
I truly don't know how thoroughly a police force investigates a suicide. I imagine it varies. I imagine they would make more effort with someone young. Especially if the parents are up in arms. If they want to know how their child got the information or sources to purchase things.
I assume they don't usually bother that much though. Think of how long sources have remained active when they must have known about them- one way or another.
But, I'm not too sure what you mean. Do you mean- will Sasu hand over your account information, private conversations etc? I don't really know. I suspect they would need to believe a crime had been committed to request that. So again, I suppose it depends on the person themselves. How suspicious was it that they CTB? Was it likely they were coerced etc?