Can you be arrested for owing money to a small business?

It depends on the following:

1) You borrowed money, purchased an item, or had the business perform work (etc.) in good faith, intending to pay or repay; however, since then, circumstances have arisen that prevent payment. This is not a crime, since you had no criminal intent (called "mens rea"); therefore, while you could be sued for the money, you could not face criminal liability.

2) You incurred the debt in bad faith, intending to not pay--that is a criminal act. Or you paid with a check you knew was bad at the time you issued it--that is also a crime. In these case, since you had criminal intent, you could face criminal liability.