N.Y. Comp. Codes R. & Regs. tit. 12, § 801.29
(c) The employer must consider the following injuries or illnesses to be privacy concern cases:
(6) other illnesses, if the employee independently and voluntarily requests that his or her name not be entered on the log. Effective January 1, 2004, musculoskeletal disorders (MSDs) are not considered privacy concern cases.
This is a complete list of all injuries and illnesses considered privacy concern cases. No other types of injuries or illnesses may be classified as privacy concern cases.