Yes....if.... If you're not a danger to yourself or others, no one will force you to accept psychiatric treatment you don't want. If its medical treatment that you are refusing, your doctor will want to make sure that you understand the treatment they think you need, what would happen if you didn't have that treatment, and would want to make sure that you have the insight/ judgment to make your own decisions.
Yes but. One can refuse voluntary psychiatric admission, but that creates a decision process as to whether or not involuntary assessment (usually for a max of 72 hrs) is needed for purposes of assessing or reducing risk of harm to self or others. After that if involuntary is needed, usually a court hearing ensues. Involuntary admission has risks of loss of rights and even has security clearance issues.