Healthcare Enhancement for Local Public Servants Act of 2009 - Amends the Internal Revenue Code to: (1) extend eligibility for tax-free distributions from governmental employee benefit plans for health and long-term care insurance to any retired state or local public employee (currently, limited to retired public safety officers); (2) provide for a tax deduction of such distributions rather than an exclusion from gross income; (3) allow nonitemizing taxpayers to claim such tax deduction; and (4) allow an annual inflation adjustment to the $3,000 distribution limit beginning after 2009.