No you cannot in Brewster. Other offices that you need an appointment, yes. In Brewster, you have to go to the office and make an appointment to take the written permit test. Then you have to go a second time a couple weeks later to actually take the test. Brewster is special in this regard. All other office in New York State only require 1 visit to the DMV office, Brewster requires 2. Like in Beacon, you don't need an appointment, you just go there and take the written test immediately. All other offices that you need an appointment for, you can make the appointment on-line, and go there once to take the written test. But Brewster is incapable of on-line appointments.
I think so, just go to the DMV Website
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