Do I need to go for a Covid-19 test if I was in contact with a positive tested person at work?

Possibly. What was exposure like? Were you close to infected person – less than 2 meters? Were you both wearing masks? Did the person appear ill? Sneeze or cough near you? Interaction less than 10 minutes? In a crowded or poorly ventilated room? – (vs being outdoors). Even if answer is “no” to many of these questions, a direct cough or sneeze can get infect you.
Yes. One indication for testing is an individual who has had close (i.e. within six feet) or proximate contact with a person who is known to be positive with COVID-19. So I suggest you get tested for Covid-19. I wish you well with your health! .