What right does the accused have with regard to who determines his/her legal guilt or innocence?

Depends on the type and severity of the crime, on the laws laws of your unknown country and, if it's a Federal country, on the laws of your unknown State or Province.

The accused may, or may not, have the right to a trial by jury, and if he has that right he may, or may not, have the right to request a trial by a judge (or panel of judges) instead.