J.P. Morgan Chase & Co. Chief Executive James Dimon, already frustrated with some aspects in the Dodd-Frank law, is questioning whether the Federal Reserve Bank of New York’s implementation of a provision will allow him to perform his duties on the Fed board. The issue came to a head Thursday, when Mr. Dimon raised the issue at a New York Fed board meeting, said people with knowledge of the meeting. Mr. Dimon and other bank representatives on the board could end up resigning, though the issue remains unresolved, these people said. The Dodd-Frank law passed by Congress in June bars bankers from having any say in the selection of the presidents of the 12 regional Fed banks. But the New York Fed is considering restrictions that go beyond the Dodd-Frank law, including rules on other appointments and access to information.