I do loans in NY and can pay your closing costs if you will accept a higher interest rate - they aren't "rolled in" to your loan amount but they are paid for us by giving you a "lender credit". The lender credit is generated by giving you a higher interest rate than what you qualify for if you didn't want the lender credit. I just priced it out on our rate system and as of today with a 660+ score we could give up to a 2.750% lender credit towards your costs (640-659 score it drops down to a max of 1.750% in lender credit, and 620-639 score a 0.750% max lender credit). It can be credited towards our lender fees, appraisal fees, insurance/tax escrow account, initial 1-year of insurance, pre-paid interest, attorney/title fees, recording fees & transfer/mortgage tax, pro-rated amounts owed to seller for taxes and pretty much anything else that is owed from you at closing (other than your down payment). We just did this for someone in Waywayanda, NY earlier this year and will be doing it again this month for someone in Binghamton, NY.
Our pre-approvals are pretty in-depth and require checking credit & reviewing your income & asset documentation + anything unique about your situation... even will go so far as to have it reviewed by an underwriter if needed.