There is no blood test that can confirm or deny if someone is suffering from PMS. It would be nice if there was, but such a test simply doesn't exist. For a long time, people would test sex hormone levels (like estrogen and progesterone) are various points in the menstrual cycle for clues, but sex hormone levels are largely the same in people who have PMS and people who don't. There are other reasons to test these hormones but they don't diagnose PMS.
So if you can't diagnose PMS with a blood test, why run one?
Because of PMS mimicking conditions. In this post, I talked a bit about some examples of conditions that act like PMS and some conditions that are worsened by PMS. Some of these conditions can be ruled out with simple, inexpensive blood tests. Not all of these tests are applicable to all PMS patients.
Hypothyroidism can usually be ruled out with a TSH test
Anemia (common in people who menstruate) can be ruled out with a CBC and Ferritin
Prolactin can be tested to rule out a prolactinoma, which is a rare condition.
Vitamin D could be run to find a deficiency which can make PMS symptoms a bit worse. Vitamin D deficiency is common in Canada.
FSH can look for pre-mature ovarian failure and menopause which is relevant in some cases.
17-OHP can help detect congenital adrenal hyperplasia. Is condition is rare.
Testosterone and blood glucose measures are sometimes tested to look for PCOS.
Sometimes estrogen and progesterone are useful to find information about the menstrual cycles, fertility, pregnancy and development through puberty if issues arise. Progesterone is useful to confirm ovulation is occurring. Some people are reassured by testing these hormone levels.
I have never needed to order all of these tests for one patient. Typically there are a few, that based on symptoms will seem the most relevant for a patient. The first 4 listed are commonly ordered. There are others that come up depending on what patients are experiencing that are not listed here.