Connecting Our Medical Providers with Links to Expand Tailored and Effective Care or the COMPLETE Care Act This bill modifies payments and establishes certain requirements to support integrated behavioral health services under Medicare. Specifically, the bill increases payments for integrated behavioral health services that are provided by physicians under Medicare for 2025-2027, with payments increased by 175% in 2025, 150% in 2026, and 125% in 2027. The bill also requires the Centers for Medicare & Medicaid Services (CMS) to establish reporting requirements for physicians and practitioners who participate in certain alternative payment models under Medicare in order to measure the extent to which behavioral health services are integrated into primary care under these models. The bill provides funds for FY2024-FY2027 for the CMS to contract with entities to provide technical assistance to primary care practices that want to adopt models for behavioral health integration.