Nursing-facility coverage in New Jersey lives inside the same MLTSS structure that covers every other long-term-care setting. DMAHS uses managed-care organizations to coordinate everything, and the program can deliver comprehensive services in a nursing home just as readily as in a person's own home, an assisted-living facility, or a community residential setting (New Jersey MLTSS overview).
Clinically, an adult has to meet nursing-facility level of care to qualify — defined as needing hands-on help with three or more activities of daily living, or having cognitive deficits that require supervision and cueing across three or more of those same activities. Financial eligibility is assessed separately from that clinical test (New Jersey MLTSS clinical criteria).
New Jersey's Division of Aging Services runs the process for actually getting Medicaid approval for long-term care — Pre-Admission Screening, or PAS — through Long Term Care Field Office counselors statewide. PAS is the care-needs assessment for anyone applying for Medicaid-reimbursed long-term care, whether that's in a nursing facility or through a home- and community-based alternative (New Jersey PAS overview; New Jersey Community Choice).