The New York Court of Appeals, New York's highest court, has ruled that a bicyclist injured by a dog crossing his path in Central Park has no right of action against the dog owner. This is true even though the dog had no business in the roadway. The cases are Doer v. Goldsmith and Dobinski v. Lockhart.
Here is the link to the full decision, including concurrences and dissents. http://courts.state.ny.us/ctapps/Decisions/2015/Jun15/17-66mem15-Decision.pdf
The problem is that New York follows the rule that there's no claim
against the dog owner for injuries the dog causes unless the dog has been
shown to have "vicious propensities", meaning it's bitten someone
before. This decision cites case law holding that the owner's violation
of the local leash law makes no difference--which is different from the
usual rule, that if you injure someone in the process of breaking the
law (speeding, for example), that's negligence per se. What someone
needs to do is get the state legislature to overturn this rule legislatively. Particularly with the clowns we have in charge in
Albany, that's not going to happen any time soon unless one of them, or
their family members (or wealthy contributors), gets bitten during dog hours. Until then, the best advice is to stay away from New York City parks during that time or anywhere near it.