INDIANAPOLIS (WISH) — Cities and towns would face limited zoning authority over some types of housing under legislation a House panel approved Tuesday morning.

House Republicans’ top priority bill this session is a measure that limits local governments’ ability to regulate the construction of some types of housing. It’s part of Republicans’ push to reduce the cost of living, in this case by increasing the housing supply through fewer regulations.

Under the bill, cities could not require public hearings or discretionary zoning for single-family homes or accessory dwelling units in residential zones. Religious institutions would be allowed to build affordable housing...