Maybe you want a full-service bank. Or you need business checking. Knowing these needs will save you from getting dinged by ATM or other fees. That's why checking out CD rates at your home bank makes sense, especially if you have more than one account there.

"Money talks," says Cummings. "Ask if (the bank) can do better on interest rates if you're already a customer."

Some people also like the personal touch that online CDs don't offer. For example, if you have an account at Bank of America, you can go into the branch and get a problem resolved or a question answered.

So make sure you learn the process for working with an online bank before signing on. You'll want to know how you get your money back, how you make deposits and how customer services works.

You may be a prisoner of snail mail. Don't forget that funding your CD by mail can take several days versus just taking a deposit to your local bank.

"How easy is it to work with the bank?" says Hopwood. "Do you have to wire money or send a check? How do you get your money back?"