Hi and welcome to Just Answer! I'm happy to help with your tax questions. If you need clarification feel free to ask:
Annual Exclusion for Years:
New York State does not have a gift tax.
New York State's gift tax was repealed for years beginning January 1, 2000 and after. You could give a gift of any amount and it would be taxable in New York State. Keep in mind that gifts over the federal annual exclusion amount will eat into your lifetime exemption of gifting (currently set at $5million, but had been $1million for many years prior to 2010).
For years 1999 and prior, the annual exclusion for New York State was $10,000.
Correct, if you gave a gift under 10,000, it would need to be reported in New York State.
And to clarify, gifts are not taxable income. Gift tax is a tax that the giver of the gifts pays if their gifts to any one individual exceeds the annual exclusion. There is a separate Gift Tax return that would need to be filed in the event any gifts were above the exclusion. The federal form for this is Form 709. For New York State, it was form TP-400.
I apologize - there was a typo in my response. I forgot to include the word not. It does NOT need to be reported.
You correct, if the gifts are under the exclusion, it does NOT need to be reported by either giver or receiver.