It's okay to cast genders in a way that works best for your needs. For example, Detective Biddle can be played by a female, and how funny would it be to see Ella Mentry played by a guy in a blond wig? For that matter, the entire play could be played by an all male or all female cast. It's all about having fun.
With that said, this play can be produced with as few as 16 cast members or as many as 52.