Do I allocate interest income to a state when I am a non-resident and based in an international country?

It depends. If the interest income you earned is derived from a New York (NY) financial organization and you established your account there, then it is taxable to NY. If not, then only report your rental income from  property situated there.

Thank you. It’s a bit confusing as interest income is from a CD in JP Morgan Chase which is a national bank. Accounts were established long time ago partly established in Midwest and partly in NY. I was not a U.S. resident during the year. With this context what should I do ? @DianeW777 

Since you were not a resident in New York (NY) during the year, then you are not required to report the interest earned during the year. As you indicated JP Morgan Chase is a national bank.

New York source income (for nonresidents) does not include the following income even if it was included in your federal adjusted gross income:

• certain pensions that are exempt from New York State taxation by reason of U.S. Code, Title 4, section 114 (see line 10 instructions), and annuities and pensions that meet the New York State definition of an annuity, unless the annuity is employed in or used as an asset of a business, trade, profession, or occupation carried on in New York State;
• interest, dividends, or other income from intangible personal property, or gains from the sale or exchange of intangible personal property, unless the intangible personal property is employed in a business, trade, profession, or occupation in New York State;

@rahulv85