Assuming this is a sourdough starter (you posted in the bread forum), provided there is no mould then it is probably fine. I've kept mine in a sealed airtight container in the fridge for literally over a year now and it has been fine. Just wake it up (being to room temperature), feed it and watch it come back to life. It may take a day or two especially if your house isn't that warm.
Keep an eye on it and if it smells off at any stage you'll know. Any mould of any kind and it's off, etc...
Sourdough starter doesn't need to be fed frequently if you're not using it. In fact it seems to gain flavour from storage in my experience.
The longer it is kept in the fridge, the darker the liquid on the top provided that liquid remains a clear liquid, not cloudy, mine starters have been fine.
As a back up I also keep a small amount (2 or 3 large ice cubes) in the freezer. This doesn't actually kill it, just keeps it dormant. So I have the mature version in the fridge that needs waking before use and the younger version in the freezer in case anything happens to the other.
This way I can keep several starters with different bases going (spelt, wheat flour, or rye flour) and each tastes different. I just pull out the one I want to use a few days in advance and wake it up with whatever flour it has always had.