There is no general requirement in the law to provide anyone vacation or sick days; that is, employers do not have to provide these days, and, if they should voluntarily choose to provide them, may set the criteria or qualifications for them  (e.g. how many hours are necessary).Whatever criteria your employer sets have to be applied consistently and even-handedly--so if you work enough hours to meet their standards, you would get these days, for example, regardless of whether you are called "part time" or not. There is no way to determine your eligibility without knowing your company's criteria.