(a) Notwithstanding any other provision of this part, except as provided in this section and in Sections 814, 814.2, 855, and 855.2, a public entity is not liable for:
(1) An injury proximately caused by a patient of a mental institution.
(2) An injury to an inpatient of a mental institution.
(b) Nothing in this section affects the liability of a public entity under Article 1 (commencing with Section 17000) of Chapter 1 of Division 9 of the Vehicle Code.
(c) Except for an injury to an inpatient of a mental institution, nothing in this section prevents recovery from the public entity for an injury resulting from the dangerous condition of public property under Chapter 2 (commencing with Section 830) of this part.
(d) Nothing in this section exonerates a public employee from liability for injury proximately caused by his negligent or wrongful act or omission. The public entity may but is not required to pay any judgment, compromise or settlement, or may but is not required to indemnify any public employee, in any case where the public entity is immune from liability under this section; except that the public entity shall pay, as provided in Article 4 (commencing with Section 825) of Chapter 1 of this part, any judgment based on a claim against a public employee who is lawfully engaged in the practice of one of the healing arts under any law of this state for malpractice arising from an act or omission in the scope of his employment, and shall pay any compromise or settlement of a claim or action, based on such malpractice, to which the public entity has agreed.