Q: Can a NY Municipality Be Liable for Failing to Provide a Crossing Guard?
Generally speaking, the answer is no, they cannot.
And the reason is (relatively) straightforward:
New York law immunizes municipalities against many kinds of liability to individuals unless the municipality specifically assumes a duty to them, or in legalese, where a "special relationship" has been created. In most cases, it is extremely difficult to establish that, and as a result, most of these kinds of cases will fail as a matter of law.