What kind of coating your polarizer has:

Look at the reflection directly from the front of a filter against the dark. The white reflection is from an uncoated filter, the magenta reflection is single coated, and the dark green reflection is from a multi-coated filter.

Differentiate between circular and linear polarizer:

To distinguish a Circular Polarizer from a Linear Polarizer, turn the filter backwards and look through it into a mirror. If the filter image in the mirror is black, you have a circular polarizer. If the image is clear, you have a linear polarizer.