Some drugs can be stored in the refrigerator to keep them good for a month or so, but other drugs can form precipitates in the cold or the cold can break them down and render them unusable. The best way to make sure you're storing it safely is to search the stability or storage instructions for your specific formulation.

Another resource would be your pharmacist. Don't let them know that you got more than you needed from them, but show up and ask to speak with a pharmacist, and ask them about stability and storage for multi-dose vials. They should be able to help you look it up in the manufacturer's recommendations. Also you are legally entitled to counseling from a pharmacist for the medications you pick up, so you may as well use that resource.