I have purchased a little Buddha statue with the intention to send it abroad.
Do I need official papers in order to get it out of Thailand and more important to get into my country?
If "Yes", where can I get such official export papers?
TIA

If it is an original you have bought, then the shop/seller would be the one that provides a legit paper if it is allowed to take out of Thailand. If you bought it in an antique shop or a souvenir shop, then it´s a very big chance that it not authentic and a very good made reproduction.

If you can not get the paper or verification, then you will have to contact Thai customs. Get it in to your country is usually not any problem. (Depending on the country of course)

Authenticity might not be an issue.  What is authentic? Do you mean an antique?  The Thai can even have a broad definition of what is a Buddha.  I have heard of people with images of shiva having problems with packing companies and even a naga statue could be considered a holy image.  What the OP needs is an official source who can advise him and if neccesary provide the neccesary paperwork.

https://forum.thaivisa.com/topic/920832-taking-a-buddhist-statue-out-of-the-country/