Can any employee in New Hampshire be a salaried employee or do they have to be in a management position?

You don't have to be management to be salaried anyplace.

Of course. Salaried (as opposed to being paid hourly wages) is appropriate for a position that is doing office or non-manual work involving management or general business operations, and where the job requires some independent judgment. Employees in job positions such as engineering, finance, sales, marketing, and public relations are typically salaried, even though they may not be in management. There is also a requirement for minimum salary per year - $23.6K I believe.