In 2018, the cut offs for Calcutta Medical College, Kolkata under different categories (via AIQ) are as follows-
UR/General Category - 559
SC Category - 444
ST Category - 429

For complete list of all colleges in Kolkata along with their cut-offs visit - https://medicine.careers360.com/articles/neet-cutoff-west-bengal

Keeping in mind cut off varies from year to year, I would personally suggest you to aim for 570+. It is a safe score and will definitely bag you a seat in Calcutta Medical College via All India Quota (AIQ).

Thank You
Best Of Luck

Hello Shahanshah,
Exact NEET cut off required to secure a position in West Bengal medical colleges will be released tentatively by 2nd week of August 2019 by Department Of Health and family welfare, Kolkata. It will be available for all the categories and it will be a minimum marks or rank to get a good college.

For having a rough idea about the cut off and ranks you can go through the separate page for NEET 2019 Cutoff West Bengal at careers360 itself. Also I am sharing the link of the very same page with you.
Link:
https://medicine.careers360.com/articles/neet-cutoff-west-bengal

All the best !!