New York state is joining the ranks of states that allow marijuana for medicinal purposes. An executive order signed by Gov. Andrew Cuomo will grant certain patients access, but the law will not go as far as states such as Colorado, which permits the sale of marijuana for recreation purposes.

What's different about New York's plan compared to the medical marijuana programs operating elsewhere is that the state wouldn't be allowing private parties to grow and dispense marijuana on their own. Instead, just 20 hospitals would...