No, under California Civil Code Section 56.20, an employee can't be required to disclose medical information and the employer cannot retaliate against an employee for refusing to provide medical information.
Civil Code Section 56.20, subsection (b):
"No employee shall be discriminated against in terms or
conditions of employment due to that employee's refusal to sign an
authorization [for release of medical information] under this part [Section 56.20].
