If I don't provide a statement, will law enforcement assume I am guilty?
They already think you are guilty, and everything you say will only be used to support their assumption that you are guilty.
Whether you are guilty or truly innocent, it is normal to want to explain your side of the story, even though doing so usually helps land you in jail or prison. If you are questioned by law enforcement, immediately invoke your right to remain silent and have an attorney present with you. The fact that you invoked your right to an attorney cannot be brought up against you or even mentioned at your trial. Anything you want to say now can be said through your attorney, or after seeking an attorney's advice about whether it is in your best interests to provide a statement.