Most CPT certificate allows you to do consultation, assessment, program design, and training in a one-on-one situation and up to a “small group,” which is usually up to 4 people. Even then, the restriction is that you have to have individually consult, assess, and design a program of each individual of that small group. You also can’t choreograph your instructions like that of group fitness nor choreograph the workout routine to music.
Thus, a group fitness certification is required to do group fitness (due to its structure). However, sometimes the education you receive while obtaining your CPT might allow you to challenge for a group fitness certification or at least allow you to skip some modules taught in a group fitness certification course (then again, it depends on the specialization of group fitness you want to do). For example, if your group fitness certification specialization is resistance training or portable equipment, then you might already have the necessary knowledge to challenge for the certification. If you want to specialize in aquatics or spin, then you might not be able to challenge based on what is taught to you for your CPT.