The date for CUSAT CAT as of now declared is 27th of July 2020. The authorities would have surely taken the precautions and everything as they are conducting this examination where thousands of candidates will appear together. But yes it can get postponed too since covid-19 scenario is not yet neutralized as of now. So stay tuned to the official website until then keep preparing for the exam assuming 27th July to be the exam date.
Refer to the website below for more detailed information..
Best wishes. Thank you.