In this case, I'm referring to a specific encounter on a other world card. It states: "You find yourself in an ancient and abandoned temple. Pass a Luck (-1) check to find a golden statue worth $10. However, if you take it, you are Cursed."

Do you have to do the Luck check and if you pass, do you have to take the statue and therefore have to get cursed? Or can you choose not to take the statue?

The first part, the Luck check, is mandatory. If you pass, you then have the option of taking the statue and also getting the curse. If you fail the Luck check, you don't even have the option.

Not that I would take it. $10 is almost never worth getting Cursed.