SAN FRANCISCO — The California Supreme Court sounded poised Tuesday to rule that employees have a right to be left alone by the union that bargains on their behalf.

Most of the justices sounded uncomfortable with the idea of requiring employers to disclose home addresses and phone numbers of employees who have opted not to join the local union. The National Labor Relations Board and California Public Employee Relations Board have ruled that unions are entitled to the information, but several justices seemed to think such disclosures collide with California’s constitutional right to privacy.