It just may be possible with a poor credit score, although you likely won't qualify for the lowest interest rate available. The question is can you refinance on terms that make it worth your while?
Before shopping for rates, look into ways you can clean up your credit. One way may be by getting committed to paying your bills on time. Though this may be hard, making more than the minimum payments on your debt, paying off credit cards, and limiting your spending can improve your credit score in a short period of time (as fast as 30 days).
Visit www.annualcreditreport.com to obtain a free copy of your credit history and comb it for potential mistakes. You will be surprized what you may fin. You can report those errors to the credit companies and have them corrected.
Further, decreasing your debt-to-income ratio will improve your standing among lenders. The total of your monthly mortgage expenses (payments, taxes and insurance) as well as other monthly debt payments, such as credit cards and auto payments, should not exceed 43% of your gross income.
Of course, illustrating a stable income history, having liquid assets that illustrate your ability to make multiple payments on the potential loan, and having established equity in the property also increase the odds of qualifying for an attractive rate.
Remember, 20% down payment is required to avoid private mortgage insurance (PMI). And PMI will probably cost you between $50 and $200 per month, depending on the balance of your loan and your PMI rate.
Taking these steps will maximize your chances of qualifying for a loan at a beneficial rate.
Additionally, an ace-in-the-hole you should certainly explore would be government programs such as the Home Affordable Refinance Program (HARP) and the Home Affordable Modification Program (HAMP). These free programs are designed to lower the interest rates and monthly payments for individuals whose current mortgage is an excessive burden, and for people who owe more on their mortgage than their home is worth. Mortgage rates have been adjusted to as low as 2.375% through these initiatives.