Health Savings Accounts Improvements Act of 2012 - Amends the Internal Revenue Code, with respect to health savings accounts (HSAs), to: (1) allow a tax credit for retirement savings contributions for deductible contributions made to an HSA and salary reduction contributions under a cafeteria plan made by an employer to an HSA; (2) provide a special rule to allow a tax deduction for medical expenses incurred before the establishment of an HSA; (3) allow a husband and wife to make catch-up contributions to the same HSA; (4) allow veterans who receive medical benefits for a service-connected disability to participate in an HSA; and (5) allow HSA participants who are enrolled in a group health plan as a former employee or spouse of a former employee and who have attained age 55, but not age 65, to pay expenses for coverage under such plan from an HSA.