I would not be too alarmed about this. Most refrigeration systems will drip water off of the condenser coils while in use. This can most often be seen by cars that appear to "leak" only when the a/c is on. All that this "leakage"is is condensation. This is the same reason that window air conditioners need to have a slight downward tilt to the outside. This is also why they unfortunately, often freeze up.

If you're only noticing leakage while the refrigerator is running then I would bet even money that this is what's happening especially if the refrigerator is still staying cold. Most normally this condensation is caught in a drip pan which lets the water evaporate. However, during periods of extended use, especially with periods of high humidity i.e. the summer, sometimes the condensation is higher than what the drip pan can hold and you get leakage over the sides.

Unfortunately while this is a relatively minor problem about the only way you are going to eliminate this is to install a dehumidifier in your home, or simply tolerate it for a month or so during the summer. I would bet dollars to peso's that after mid august this won't be a problem.

One thing to note however, is that if you start to see that it is running constantly, or if you notice that it's not keeping cool, then it may be time to call in a service person. But for your particular problem I don't think that will be necessary.