I would not call Taihojutsu a style of Jujutsu.
What constitutes Taihojutsu is constantly changing to meet the needs of police officers. As I understand it, the first Taihojutsu program at the Tokyo Metro Police Department was comrised of Yoshinkan Aikido, Kodokan Judo and some older style Jujutsu technqiues.
You can train in Aikido and niot train in Taihojutsu. You can can train in Jujutsu and not train in Taihojutsu. Even though both makeup part of taihojutsu. What makes it Taihojutsu is the Police orientation of the training. Even Wado Ryu Karate has a syllabus of Taihojutsu techniques.
Also, what is very telling of taihojutsu not being a "style" is that no one has ranking in "taohojutsu". All the "taihojutsu" teachers you will meet, atleast if they are from Japan, have Dan grades in all sorts of things - Judo, Aikido, weapons arts, etc. But none will have a grade in taihojutsu.