Traditionally, Mumbai Police has been working mostly independently of the Maharashtra Police. In fact, previously, Mumbai Police personnel were having a separate cap (with yellow colour) and uniform. The Commissioner of Police of Mumbai used to be mostly operationally independent of the DGP (at that time IGP) of the State Police. It was way back in 1864 (about 156 years back) that a police commissioner was appointed for Mumbai Police.
It was only a few decades back that Mumbai Police got almost fully integrated with the Maharashtra Police.
The traditional logo / insignia of Mumbai still continues. There is nothing unusual in that. It happens in Army too, where different units may have their own insignias.
In fact, it is not uncommon for an organisation to have a separate logo from its parent organisation. Rather, it is quite common. For example, almost all central government departments have their own logo or insignia which is different from the central government itself. Even an organisation under another organisation (and, both under the Government) may have different logos.
Dr. Ashok Dhamija is a New Delhi based Supreme Court Advocate and author of law books. Read more about him by clicking here. List of his Forum Replies. List of his other articles. List of his Quora Answers. List of his YouTube Videos.