I'm Lucy, and I'd be happy to answer your questions today.
There is no specific law that requires an independent contractor to have a written agreement if the work is only expected to continue for 8 months. If the parties anticipated that work would continue for one year or longer, then they'd have to have a written contract before it could be enforced. N.Y. General Obligations Laws, Section 5-701.
It's not the duration of the working relationship that determines whether someone is an employee or a contractor. The determining factor is control. When the company dictates what the worker does, when, where, and how they do it, provides the tools, and other manages the work, that suggests the worker is really an employee who should get a W-2 and have taxes withheld. When a worker has autonomy to accept or reject an assignment, has set parameters but is given freedom to complete the job as he sees fit, gets to choose his own work hours as long as work is completed by a deadline, works away from the company's usual place of business, uses his own tools/supplies, that tends to suggest he's a contractor.
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