As developers plan to break ground this week on the second phase of the City Point development in downtown Brooklyn, the long-anticipated project has become a flashpoint in a simmering battle over the use of nonunion construction labor.

Developers said construction work on City's Point's 670,000 square feet of retail space portion will be at least partially nonunion, and at least some of the space for about 700 apartment units likely will be as well. The 1.8 million square-foot project is being built with affordable-housing...