People couldn’t be hired at Tesla Inc. without signing an agreement restricting them from spreading proprietary information, according to the company’s senior director of human resources for production and supply chain.

Josh Hedges, the Tesla manager, testified in a National Labor Relations Board trial Sept. 26, the first witness called by the electric-car maker as it begins its defense against allegations lodged by a regional director of the labor board. The director accused the company of violations of federal labor law including maintaining a strict confidentiality policy that infringes on workers’ rights as well as retaliating against pro-union employees.

Hedges...