Despite just closing, it may make sense for you to refinance. Ultimately it will depend on how long you're planning to stay in the home (assuming you live there) and if you have an itchy trigger finger to refinance everytime rates drop 0.25%. To determine that, lets look at a couple scenarios that you could put your situation into.
I'll put mortgage amounts here with your current payment (assuming no PMI) and what it would be next to it (since I don't know your credit, I'm going to be somewhat conservative here and say 5.25%). I'll estimate closing costs to be $2000 (with no points to buy it down for this example, break-even may vary depending on loan size and typical costs for an area)
$125,000 mortgage - $810/mo --- $690/mo -- 16.7 months break-even
$200,000 mortgage - $1297/mo -- $1104/mo -- 10.4 months break-even
$300,000 mortgage - $1945/mo -- $1656/mo -- 6.9 months break-even
$400,000 mortgage - $2594/mo -- $2208/mo -- 5 months break-even
If you're looking to sell or flip this home in less than the period corresponding with your loan amount, it's probably best not to do anything. If you're planning on staying there longer than the break-even, it probably makes sense to do something.
If you're the type of person who will want to refinance everytime rates drop 0.25%, it may be better to to take a slightly higher rate in exchange for a portion of your costs to be covered by the lender (to decrease your break-even period). This scenario works best with larger loan amounts.
Lastly, you'll need to think about where the money will come to close your new loan. Even though you just bought a home, you will probably have a month of trailing interest (that month you skipped) and your escrow account will now probably need to be "re-funded". The cost between closing and your pre-paids could prevent you from refinancing if you don't have funds of your own to bring to closing. Some lenders will "net-fund' your escrow account in your loan payoff (your payoff will decrease by the amount of your escrow balance) while others will create a new escrow account which could be quite a lot of money if you're nearing tax time. Ask these important questions. If the person you're working with can't answer them, look for someone else; There's nothing worse than the blind leading the blind.
Disclaimer: This scenario doesn't apply to everyone, please be mindful of where you are in your amortization schedule. For you, this may make sense but others it may or may not be depending on what your long term goals are. Individuals much further into their repayment will want to review their payment schedule and decide if they want to restart their mortgage again or if they'd like to structure the loan to pay it off in the same amount of time paying less interest or to simply lower their monthly obligation without regard to long-term interest accrual. This piece is too difficult to cover here with just one post, contact me directly for a personalized analysis if interested.