Since 2010, the New York State Department of Health Medicaid application form is called the Access NY Application or form DOH-4220. Download the form at this link (As of January 2021, the form was last updated in March 2015).
Do not use the DOH-4220 application for Medicaid applicants in the MAGI category (generally those under age 65 or, if younger and disabled, not receiving Medicare). All MAGI applicants should go through the NYS Health Benefits Exchange to apply for Medicaid. They can contact a Navigator or Community Health Advocates for assistance.
All local districts in New York State are required to accept the revised DOH-4220 for non-MAGI Medicaid applicants (Aged 65+, Blind, Disabled) (including for coverage of long-term care services), Medicare Savings Program, the Medicaid Buy-In Program fr Working People with Disabilities.
The DOH-4220 - Access NY Health Care application can be used for all Medicaid benefits -- including for those who want to apply for coverage of Medicaid long-term care -- whether through home care or for those in a nursing home (with the addition of the Supplement A form, described below).
Applicants who only want a Medicare Savings Program (MSP) may continue to use the MSP-only application (and this is recommended). Districts must also continue to accept the LDSS-2921, although it only makes sense to use this when someone is applying for both Medicaid and some other public benefit covered by the Common Application, such as the income benefits such as Safety Net Assistance.
See this article for more about these different Medicaid categories, and these charts of the different rules for counting income and resources for the different categories.
There are several other online resources relating to the new application - check here for changes