Health Agency Check-Up Act This bill establishes a bipartisan commission to review and recommend whether to modify or eliminate statutory reporting requirements that apply to the Centers for Disease Control and Prevention (CDC), the National Institutes of Health (NIH), and the Food and Drug Administration (FDA). To inform this effort, the CDC, the NIH, and the FDA must provide the commission with relevant recommendations and information about their respective staffing, budgets, programs, reports, and regulations. The bill automatically makes any provision of law requiring a report that the commission recommends for elimination ineffective after 45 days, unless Congress enacts a joint resolution disapproving of the recommendation.