(b) Designate a center, program, or facility other than one designated by the department of mental health and addiction services or the department of developmental disabilities, as described in division (A)(2)(a) of this section, to conduct the evaluation and preceding examination of the mental condition of the defendant. Whether the court acts pursuant to division (A)(2)(a) or (b) of this section, the court may designate examiners other than the personnel of the center, program, facility, or department involved to make the evaluation and preceding examination of the mental condition of the defendant.