A constable who is trying to serve me a summons for court for collections had a neighbor buzz him into my apartment building of 12 tenants and posted a notice on my apartment door that is visible to all stating that he needed me to contact him about him having some court papers he needs to serve me. Is this legal? How do I prove that he did this? And how should I proceed?

Yes he can do this, it is where you live ? You should contact him and get served so you know when and where to go to court. If you don't get served, they will merely serve you by other methods where you don't know when and where court is, so they have court and you lose.
This way you at least can go defend yourself.

He is allowed to ask where you are, and tell people he is there to serve papers. In some areas it is even OK, just to post the papers to your door, and that is legal service

I was asking what the law is in Rhode Island as far as this is concerned. I don't believe it would be legal to demoralize someone by allowing their neighbors to see their personal business posted on their door for everyone to read at will until the notice is removed. In my case I am not even in the state of Rhode Island, it was a neighbor that called me to tell what took place. I have no plans on returning to RI in the next couple of months.

First if you wanted the law in RI then why didn't you mention yo were dealing with RI?

This should help Rhode Island Constable Rules - Commencement of Suit (http://highconstable.com/resources/ri/rules/commencement_of_suit.php)

However, he didn't serve you yet. He simple gave you notice that he was trying to. And I doubt if there is anything illegal about that.

If you ignore this you could find yourself with a default judgment.

Yes, they can allow your neighbors "see" your business, in fact if you don't get served by service, they are likely to publish this in the news paper and do service by legal publication.

Sorry you are not happy with it, but this is how finding you works, so have you called and got the legal papers given to you yet ?