If you don’t, the criminal case against you is weaker because there’s no chemical test evidence that can be used against you.
You could be issued a license suspension for the refusal.
The police can still pursue the case based upon the common law charge of their belief that you’re intoxicated, but they don’t have the additional evidence.
The DMV ultimately will treat you separately and can pursue you for the refusal, but that occurs after the criminal case is completed.
In most instances, it is better if you don’t submit to the test unless you know that you’re completely sober and less than a 0.08 BAC.