Although this is not my area of practice, I would say it's highly unlikely. You do face having the furniture removed from your home for failure to make continued rental payments; and if you obstruct the removal, I supposed there could be a charge of breach of peace. But failure to make rental payments or pay late fees is not a crime.
If you do not let the company come into your home and they believe they are entitled to get the furniture, in most states there is a way for the company to go into court and get an order entitling them to take the furniture.
Unfortunately, rent-to-own places cater to customers in financial difficulty; the payments and late charges are high and customers in your situation often do lose their money, because you don't acquire any ownership interest in the furniture until the final payment.
Disclaimer: This site exists to provide information only. It is not legal advice. Answering your question does not create an attorney-client relationship. I am a Massachusetts lawyer. Any information provided on this site does not, except as explicitly stated, imply familiarity with laws or procedures peculiar to your state which may differ from those where I practice.
You cannot be arrested for a civil debt. I suggest that you consult with a debt counselor or an attorney who handles collection actions to determine your best defense or to work out a negotiated settlement of this issue.
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