Home and Community Services Copayment Equity Act of 2006 - Amends part D (Voluntary Prescription Drug Benefit Program) of title XVIII (Medicare) of the Social Security Act to eliminate part D cost-sharing for certain non-institutionalized full-benefit dual eligible individuals with income below 135% of the poverty line who: (1) reside in an assisted living facility, a resident care program facility, or any other appropriate licenced facility, including a psychiatric health facility, a mental health rehabilitation center, and a mental retardation developmental disability facility; or (2) receive home and community-based services in a home setting under a home and community-based waiver.