Just to give examples of two zoonotic diseases, here are some considerations in making various diagnostic choices:
Anthrax
Although microbiological media can support the growth of Bacillus anthracis, and special selective media exist to grow it, biosafety level 3 measures should be used. It does represent a health risk to laboratory workers. More sophisticated testing to identify B. anthracis is recommended, such as MALDI-TOF-MS or PCR. The CDC's recommendation for how a typical laboratory should handle a suspected anthrax is below.
Rabies
Rabies in a live person is most often suspected by clinical presentation and history. Multiple tests are recommended on someone before death. Appropriate specimens are saliva, serum, spinal fluid, and skin biopsies of hair follicles in the neck. Saliva can be tested using virus isolation or RT-PCR. Serum and spinal fluid can be tested for antibodies to the rabies virus. The skin follicles can be tested for the rabies antigen.
Many techniques are available to identify rabies in animal and human post-mortem specimens. For example, brain tissue can be tested with direct fluorescent antibody tests, immunohistochemistry, electron microscopy, and amplification techniques. These tests are usually performed in state health labs or other specialized testing laboratories.
Others
Many other types of zoonotic diseases such as Campylobacter, Salmonella, and others can be identified using routine methods in typical microbiology labs.