The short answer is that there's only one way to tell whether this will be an impediment... ask a few companies whether they will issue a bond with that record in your past. Chances are that this may not be an absolute prohibition to starting a cleaning company but I would be surprised if any of the more lucrative contracts did not require bonding and insurance. Nonetheless, do not lie on the application as that could have much worse consequences if it ever came to light. Good luck.
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I have a provided a link to an article about starting a cleaning business in New York that you may find helpful.
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