They would need to give a Blood sample. If someone gives a blood sample, whoever is testing it, can tell a large number of things. (ex. if you're dehydrated, how many red blood cells to white blood cells ratio, if you have a vitamin deficiency, and a ton of other things.) They will be able to tell how long you've been exposed to something poisonous because they will be able to see the changes that the poison has made to the blood stream, and the way it affects it.
Hope this helps!! (: