I did a refi about a year ago. It was a nightmare - I wanted to hang myself.
Not only do you need to look at your credit score, but you also need to consider your income to debt ratio. I had two part time jobs at the time. The company I went through was only counting one of my incomes so they made me pay off the only credit card we had (that was the only debt we had). I couldn't understand why we had to do that, but I did it anyway. That in itself was a nightmare. They wanted all kinds of bank statements to show that I had the money I used to pay off the card, then they needed documentation of the step by step process of transferring the money from my savings to my checking, then the check from my checking account to the creditor and then a new statement from the creditor that reflected the pay off. Of course, they didn't tell me this until just few weeks prior to closing so getting all of the documentation was tricky. They were soooo picky about what documentation they would accept. I found myself at the bank pretty much daily - sometimes more than once! My bank even called them because it was so ridiculous! And to find out at the very end that the reason I had to do this was because they erroneously neglected to consider my second income sent me over the edge. Had they looked the documentation submitted to verify income, they would have seen that I had two different employers and my income was twice what they thought it was, I would not have had to pay off that credit card.
Also, the closing costs. You do need to have this money and can prove that you've had the money for a couple of months. So, if you're planning to borrow money to pay closing costs, you have to have a note from the lender saying it's a gift and you don't have to pay it back, and then 3 months of THEIR bank statements to show that they had the money to lend.
We were going to pay closing costs out of cash that hubby and I had earned and squirreled way doing side jobs. WRONG! They won't take cash; you have to prove the source of the funds you're using to pay the closing costs. So, we had to pretend to borrow from my brother-in-law. And then we had to go through the process described in the preceding paragraph.
I guess if you have a great credit score, keep all your money in the bank so it can be traced, don't have much debt (or at least a good income to debt ratio), and can pay closing costs with money already in the bank, you'll be fine.
I wish you the best of luck. I've told my hubby that unless interest rates are lowered to zero, I will NEVER do that again!