It looks like NY offers a strong incentive and a categorical program for full day kindergarten but I couldnt find a law that says it is mandatory. Indeed a chart at the end of the pdf says that the kindergarten laws are permissive instead of mandatory like in a number of southern states.  Indeed Lousiana not only do districts need to fund full-day kindergarten but pupils must attend as well.  New york it doesnt say so, so I presume there is no law.
 
From the attached pdf:
 
Because most states do not mandate district provision
of full-day kindergarten,there is currently a large variation
in distribution of access within most states.When surveyed
by ECS for this study,many states did not know the
percentage of school districts that offer full-day kindergarten.
For those states that do track this data,two states (Montana
and New Hampshire) report that fewer than 10% of school
districts offer full-day kindergarten;while another eight states
(Delaware,Florida,Iowa,Missouri,New Mexico,New York,
Virginia and Wisconsin) report that more than 70% of
districts offer full-day programs.
 
...
 
A strong incentive for school districts to offer full-day
kindergarten exists when the state provides more funding
for full-day kindergarten than is provided for half-day
AND when the weight provided to full-day kindergarten
is equal to or greater than the weight provided to 1st
grade.This definition assumes that full-day kindergarten
requires a similar,or greater,level of resources as 1st
grade and that the state is willing to provide this level
of funding to all school districts.Seven states provide
a strong incentive to offer full-day kindergarten (Alaska,
Georgia,Illinois,Nebraska,New Mexico,New York
and Wisconsin).
 
...
 
Three states (Massachusetts,New Hampshire and
New York) use categorical programs to target funding
to districts that have never offered full-day kindergarten
programs in the past.
 
Hope that helps.