China’s two biggest cities tightened Covid-19 curbs on their residents on Monday, raising new frustration and even questions about the legality of its uncompromising battle with the virus.

As authorities wrestle with China’s worst Covid-19 outbreaks since the epidemic began, authorities in hanghai have launched a new push to end infections outside quarantine zones by late May.

While there has been no official announcement, over the weekend some residents in at least four of its 16 districts received notices saying they were no longer able to leave their homes or receive deliveries as part of the effort to drive community infections down to zero...