What is digging these holes in my flower bed?

Today I went out for my morning smoke and found four identical holes in my flower bed, each about 3x3 inches wide. I live in northern Kentucky so my guess is that they are either from moles or chipmunks, or possibly even small ground squirrels. Which of these animals is it, and can they damage the roots of my plants? The holes all seem to be against the edge of my flower bed, so it doesn't look like they are under my plants- yet. I want to get rid of them somehow, but I'm a vegan and animal rights advocate so I don't want to put the animals in danger or destroy their homes by filling them in. Can I somehow humanely relocate them away from the flower bed?