What type of law does medical error fall under, criminal or civil?

In the states, if a patient dies unexpectedly, say during a routine operation, is there any police involvement in this case? I assume that such matters are handled under civil law, with involvement of the law/courts only if a patient or their family brings suite, and that it would be handled as a civil, not criminal, case.

Medical MALPRACTICE is a CIVIL issue. A medical ERROR, may or may not constitute malpractice. A patient dying unexpectedly, even during a 'routine' operation, may or may not involve a medical error. This would only be a criminal issue if someone deliberately caused the death or was EXTREMELY negligent.

That is correct. A criminal suite would only be taken if there was gross negligence involved and intent to commit bodily harm resulting in death to the patient.

Medical malpractice law and unless there are grounds to believe the death was other than a result of the surgery, the police are not involved.

If, upon later finding, a mistake was made that resulted in the loss of life and the physician and/or hospital covered up that fact, then the police could be involved for criminal conspiracy investigation.

Generally, medical malpractice is a civil case. Occasionally there might be a police investigation as to whether it was more than a medical error, such as intentionally assisting in ending a patient's life in the manner of Dr. Kevorkian. While many people consider there are cases in which that is within ethical conduct, it is illegal in all states except Oregon.