Is REST API Possible with Codeigniter?

That is a good tutorial.
...
Is it maintained by codeigniter?

CodeIgniter does not include a REST API so no, the tutorial is not maintained by CodeIgniter.

Is it safe to use in my projects?

What do you mean by safe?

As far as it goes the code should work but I would say there are problems. The main one being that user input is being trusted without being verified or sanitized. Never trust user input! There might be other issues but I did not examine the tutorial in depth.

From my point of view there is some coding there that (at best) points to a less than full understanding of CodeIgniter or (at worst) indicates a thoughtless approach to coding. For instance, this bit of code.

PHP Code:

  //API call - add new book record
    public function add($data){

        if($this->db->insert('tbl_books', $data)){
           return true;
        }else{
           return false;
        }
    } 


The if statement is totally unnecessary. Since index() returns true or false why use the if conditional? Instead, simply return the results from index().

PHP Code:

  //API call - add new book record
    public function add($data){
        return $this->db->insert('tbl_books', $data));
    } 


And again the input is accepted "as-is" which is far from a best practice.

To be fair, it's important to recognize that the tutorial is not presented as complete and robust production level code. It simply demonstrates basic concepts.

But missing the security part.
How to give access to the specific user only? OAuth?

You are asking about Authentication which is a separate concern from REST API.

There are many third-party authentication libraries build for CodeIgniter. Community Auth and Ion_Auth are but two that are in wide use. There are others and also lots of examples on how to do-it-yourself. Any of these could be integrated using a RESTful API.