Snapchat will certainly be collecting a lot of data on you. But even without that, it'd probably be easy to get an idea of who it is from how they registered the account. Furthermore, the usage and so on of that account can give away a lot on the person behind it.
Having said that, to get access to such information, the police would have to request it from Snapchat under the right conditions. Things like Terrorism, Immediate Threat to Life and various other sneaky government matters will have Snapchat hand over the data, no problemo.
Some kid in school pretending to be you and said some mean things that upset you. Absolutely not.