Is it possible to detect if a player owns a certain item such as a hat?

Much like in 'Trade Hangout', I need to make a script that detects if a player owns a certain hat on the website. The catch is that the player does not necessarily have to be wearing the hat in the game.

We know that it can be done with limited hats & gear because we can see it on 'Trade Hangout'. However, I was wondering if it could be done for non-limited items too.

If you could shed some light on this topic I would greatly appreciate it!