Do postdoctoral doctors need the signature of a co-tutor to apply for a patent?

It is your own right to apply for a patent, but if the patent is completed in cooperation with others, especially under the guidance of a tutor, you can't apply for a patent alone without the consent of the tutor. In addition, this patent belongs to service invention, which means that the patentee belongs to your research institute, and you can only be the inventor.