New York State and Local Municipal Law prohibits "illicit discharges" to storm sewer systems. Pet waste thrown in storm sewers, bagged or un-bagged, is an example of an illicit or "illegal" discharge that is punishable by fine and/or imprisonment.
Pet waste dumped into storm sewers can contribute to increased pathogens (i.e. fecal coliform bacteria) to surface water resources or to adjacent storm sewer systems.
The best way to discard pet waste is to either flush it down the toilet (without the bag, of course) and throw the bag in the trash.
The next best approach is to discard the bagged pet waste directly into your outdoor garbage can or separate, smaller, trash can with plastic liner.