Hurricane and Tornado Mitigation Investment Act of 2013 - Amends the Internal Revenue Code to allow individual and business taxpayers in certain states a tax credit for 25% of their qualified hurricane and tornado mitigation property expenditures up to $5,000 for any taxable year. Defines such expenditures as expenditures in a dwelling unit to improve the strength of a roof deck attachment, create a secondary water barrier, improve the durability of a roof covering, brace gable-end walls, reinforce the connections between a roof and supporting wall, protect against windborne debris, or protect exterior doors and garages.