I know this is an old thread, but it's a top google search result, so I thought I'd add in some clarification for the Cornell info:
"A producer selling eggs of his (sic) own production directly to consumers is exempt from grade and size labeling requirements."
The full guidelines as of 2009 (I can't find any updated guidelines on ny.gov, but I assume they haven't really changed) for selling your own eggs directly to a consumer:
Cartons and cases must be marked with:
1. The word "eggs".
2. Count – may be expressed in dozens
3. Your name, address and zip code
4. The words "keep refrigerated" or similar designation
5. “To prevent illness from bacteria: keep eggs refrigerated, cook eggs until yolks are firm, and cook foods containing eggs thoroughly.
Leakers, blood spots, meat spots and other type of loss may not be sold for human consumption.
Federal law requires all eggs to be refrigerated and held at 45°f or below immediately after packing, including during transportation and retail
<End Cornell info>
Notably, I do not see a requirement that the eggs be washed, but as a general rule unwashed eggs do not need to be refrigerated, while washed eggs do. That said, all eggs sold in the US must be refrigerated from packing through sale, and sold stating that they require refrigeration, even if they aren't washed (vs. Europe, which is the opposite - eggs are unwashed and unrefrigerated).
There's also no licensing requirement unless you have many many chickens (3,000 or more).