If you have a high debt-to-income ratio, it may be a bit harder to refinance but you may be able to find a lender who is willing to work with you. This is especially true if you have other more favorable elements of your application that can assure the lender that you are not a credit risk.
For example, a lender may be willing to overlook a high DTI if your income is high and your credit score is good or excellent. Some lenders are now approving applications with a DTI of all the way up to 50%.
However, if you have a very high debt-to-income ratio and are still having trouble obtaining financing, you may be able to apply using a cosigner or take steps to improve your financial situation and try again in a few months. When your high DTI improves, either by an increase in income or a decrease in your debts, you should then be able to get approved for a refinance.