If you pay someone to work in your home, such as a babysitter or housekeeper, you may be a household employer who has to pay employment taxes.
A person you hire through an agency is not your employee if the agency controls what work is done and how it is done. This control could include setting the fee, requiring regular reports, and providing rules of conduct and appearance. In this case you do not have to pay employment taxes on the amount you pay. But if you control what work is done and how it is done, the worker is your employee. If a worker is your employee, it does not matter that you hired the worker through an agency or from a list provided by an agency.
To find out if you have to pay employment taxes, see Publication 926, Household Employer's Tax Guide.