My wife and me are international students and have F1 visas. My wife is a resident alien, lives in MN. I am a non-resident alien live in NY. We intend to file the tax under "married jointly" category. We decided to file my status as resident as of Publication 519 for Federal return. My problem is what form should I select for NY state return. Can I file IT_203 form as a "married filing separate" for this?

You can jointly for BOTH states, but pay taxes ONLY on income earned within the state borders.

My wife and me are international students and have F1 visas. My wife is a resident alien, lives in MN. I am a non-resident alien live in NY. We intend to file the tax under "married jointly" category. We decided to file my status as resident as of Publication 519 for Federal return. My problem is what form should I select for NY state return. Can I file IT_203 form as a "married filing separate" for this?

1. Please explain: Your wife is resident alien as well as on F1? How does she qualify to be a resident alien?
2. You can only file resident tax return as Married Filing Jointly. Then all your income during F1 will be subject to FICA taxes. You lose your exempt status.

My wife is resident under the category of "substantial presence" for F1 status. That is she has been living here for more than 5 calender years in the US

For federal tax return, you can file resident tax return as Married Filing Jointly and you lose exemption during F1. Second choice is that your wife files as Married Filing Separately (resident return) and you file a nonresident return.
For state returns AtlantaTaxExpert has already explained.