I'm considering refusing the admission of NYU because of no scholarship. If I reapply next year, will it consider that I rejected it once？

I can ask for deferral. But can I still apply for scholarship in the next year? If I ask for deferral, can I apply for other law school in the next year?

I think that if you ask for a deferral,you cannot apply to other law schools next year.
As for the scholarships,I have no idea,but I'd strongly suggest that you contact them and make it clear.You do not want to be left out of scholarships,since this is the reason you are not going this year.

call them, write them a letter to explain that you are in a difficult postion then if you do apply next year you can always said that now you have founds some funds and it will look better that saying nothing and just refuse.