Are you talking about cancer marker blood testing, endocrine testing or ?
Even cancer marker testing aren't 100 percent accurate, and I don't know if they have that kind of testing for cancerous brain tumors.
There are a number of tumors, including what they call a non-functioning adenoma of the pituitary where blood tests might not reveal anything (this is a kind that can often become a macradenoma, which is a large pituitary tumor). Meningioma is another example of a tumor (a brain tumor grows on the lining of the brain and can start putting pressure on the brain if it grows inward) where I know of no blood testing that would demonstrate it was there.
On the other hand, tests that come back abnormal, like the ones enzymelover mentioned and more could signal the doctor to order a dynamic pituitary MRI with and without contrast.
If you are having neurological symptoms, a CT scan or MRI of the brain is what they use to find brain tumors, but the pituitary takes a separate MRI, because it is such a small gland and general MRIs of the brain might miss a tumor there.
It depends on the test. For a pituitary tumor, doctors would look at prolactin, TSH, ACTH, LH, cortisol, growth hormone, and a few other things. For various other brain tumors, blood tests might reveal nothing.