Houston Mayor Sylvester Turner announced Monday that city employees will be required to mask up in areas inside city buildings where social distancing is not doable, such as bathrooms, elevators and conference rooms. Credit: Mark Felix for The Texas Tribune Sign up for The Brief, our daily newsletter that keeps readers up to speed on the most essential Texas news. Local mask mandates are popping back up across Texas â even as Gov. Greg Abbott has stressed that local officials who try to enforce restrictions aimed at reducing spread of COVID-19 will be penalized. Houston Mayor Sylvester Turner is the most recent to defy the governorâs order. He announced Monday that the cityâs nearly 22,000 city employees will be required to mask up inside city buildings where social distancing is not doable, such as bathrooms, elevators and conference rooms.