You do not mention if it is public housing or new construction...they may have different regulations.
There are definitely rules about lead based paint, I could not find anything about oil paints..I do know that in recent years there have been state regulations about the VOC content of paints and most paint sold today has to conform to that.. You might call 311 or visit the city website at: http://www.nyc.gov
Below are some other links to housing resources where you might be able to find more info including a link about lead paint guidelines.
Hope this helps!
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