Generally, public entities are immune from liabilities for injuries to or by prisoners.
Gov.C. § 844.6(a)
“Notwithstanding any other provision of this part, except as provided in this section and in Sections 814, 814.2, 845.4, and 845.6, or in Title 2.1 (commencing with Section 3500) of Part 3 of the Penal Code, a public entity is not liable for:
(1) An injury proximately caused by any prisoner.
(2) An injury to any prisoner”
However, public employees are not shielded from liabilities for injuries legally caused by their “negligent or wrongful act or omission.”
Gov.C. § 844.6(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.”
They are also liable for failure to furnish or obtain medical care for a prisoner who they know, or have reason to know, needs immediate medical care. The liability is limited to situations where the public entity intentionally or unjustifiably ignores serious and obvious medical conditions.
Gov.C. § 845.6
“Neither a public entity nor a public employee is liable for injury proximately caused by the failure of the employee to furnish or obtain medical care for a prisoner in his custody; but, except as otherwise provided by Sections 855.8 and 856, a public employee, and the public entity where the employee is acting within the scope of his employment, is liable if the employee knows or has reason to know that the prisoner is in need of immediate medical care and he fails
to take reasonable action to summon such medical care. Nothing in this section exonerates a public employee who is lawfully engaged in the practice of one of the healing arts under any law of this state from liability for injury proximately caused by malpractice or exonerates the public entity from its obligation to pay any judgment, compromise, or settlement that it is required to pay under subdivision (d) of Section 844.6”
To know if a public entity has liabilities for injuries sustained while by a prisoner, it is best to consult with a lawyer who is an expert in personal injury cases.