How do I declare not responsible for others debts

Why would anyone think you are responsible? But generally you take an ad in the legal announcement section of your local paper.

This can vary by state ( or by country since we don't know where you are at) and whose other debts,

And of course merely declaring you are not, does not mean you are not responsible if you are actaully legally responsible and held as such by the courts.

So a little more info will really help