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Yes, you can, but not everything and not always. CT scans can show that certain brain areas are underdeveloped which can lead to symptoms like depression, psychopathy (not sure, what the exact term is, there is always discussion about what to call it) or others. Also the brain has a huge capability of taking over the functions of damaged areas in other areas, so just because it might look heavily damaged it does not always concur with the clinical representation of the patient. There can literally be patients with half a brain and you would not notice apart from their brain scan. Have seen such cases myself. One of them was a miracle to the neurologists because he was a skilled worker at a bank and had a healthy family life with nearly no brain.

There have been decades of research trying to identify biomarkers and structural differences in individuals with neuropsychiatric diseases, using imaging (MRI, fMRI), electrical activity (EEG), or serum markers (blood work) . In major depressive disorder for example, there have been associations made with changes in the prefrontal cortex, thalamus, hypothalamus etc. as seen on MRI. However these findings are neither sensitive nor specific, so psychiatric/behavioral disorders such as MDD is still a clinical diagnosis.

I should make the distinction that there are some psychiatric diseases result from structural diseases of the brain. E.g. Alzheimer's disease, Lewy body dementia, Parkinson's disease, all have distinctive findings on MRI and can have psychiatric symptoms. However most people with psychiatric disorders do not have obvious neurological disease that can be identified with imaging.

There is a lot of research and development in the field, and there is a great effort in psychiatry to incorporate objective measurements to validate clinical findings. So our understanding of neuropsychiatric diseases is likely to change dramatically in the coming years, once we develop the tools to understand these disorders better.

The short answer is that we do not yet know. There is not yet adequate evidence to identify mental illnesses by way of MRI brains scan or PET scan. (CT scans have been replaced by MRIs for detailed brain imagining.)

There have been many small studies over the years trying to answer your question. Studies are ongoing. This article explains in non-technical terms why past studies are insufficient to come to reliable conclusions and what is happening to try to get answers to questions like yours:

https://news.yahoo.com/george-santos-married-woman-while-161923713.html?guccounter=1&guce_referrer=aHR0cHM6Ly93d3cuZ29vZ2xlLmNvbS8&guce_referrer_sig=AQAAAM7gyZ-j7rRPH_Mslo4CKHIALYgVLdSvFlezFrMcwSa1x9b9X10uzkzrVrSNAQdaltWrRrfFx2dfHoXncbKBAoeUlV-lsSBj6J1ZYRepJENCl8lY5DtZwI8eZQ7DVGHBX1G5xl6yRHti1_VgtSi2QH0Ol7vkN4g5TDIWifZjvjIV

Note that this author seems to think that "depression" is more primary than brain physiology. Depression is a basket term for symptoms, not an underlying physical illness diagnosis. On a brain scan you can find things like inflammation, which is not mentioned in teh DSM at all, but you can fix mental health problems by addressing inflammation.

Quick add-on: Test specificity is how good it is at a positive result being a true positive result (not false positive). Sensitivity is the same for negative results (true negative, not false negative). A test with good specificity and/or sensitivity can be useful as a tool. Worse sensitivity and specificity make it less useful.

Aren't psychiatric disorders subjective - on the level of one's 'private' personal perception of the world? How does "objective measurement" help understand the cause and effect of something that appears on the subjective level? Can we be sure it originates at the material level?