Can a professor accuse a student of cheating on an exam without witnessing it firsthand? Can a professor accuse someone of cheating after checking his or her test? How is that possible, if the professor has not caught the student cheating red-handed?
Generally speaking, the answer to your question is "Yes."

If there is a strong similarity in answers that is highly unlikely if the students worked independently, it can raise suspicions of cheating.

For example, in Reilly v. Daly, 


  At the conclusion of the exam period, the professors held the exam papers of Reilly and the neighboring student in order to determine whether their answers matched. A comparison of the exams revealed that the first seven pages, which included twenty-seven multiple choice and matching questions, were identical.
  
  ...
  
  Taking the conservative approach of comparing only wrong answers on only the multiple choice questions, the professors were advised by a statistician that there was a one in 200,000 probability that such a match of wrong answers on the multiple choice questions would occur by chance. 
  
  ...
  
  Reilly also presented her own statistical analysis of the exam and brought to the professors' attention the possibility of "lure" questions on the exam which would heighten the probability of the match occurring by chance. The professors thereafter obtained a new statistical analysis taking into account "lure" questions on the exam. This analysis demonstrated a one in 500 to one in 5000 probability of the match occurring by chance.


Whether this kind of evidence is enough to initiate disciplinary proceedings, and what the consequences could be, depends entirely on the detailed specifics of the scenario and the university policy. 

For example, in Papelino v. Albany College of Pharmacy vs Union University, while similar statistical evidence raised suspicions, it was not considered sufficient to conclude that the students had cheated.