The APIs I'm currently using return NULL in case of false and 1 in case of true in one sub array. Returning 404 is not ideal as it refers to "address not found" and implies that the guy has requested for a wrong url. I recommend returning code 200 even and always return an array with query information (number of records, pages, etc) and a sub array in the end containing the data.
So, if you make a request to your API and it checks that there is no record to be returned, the user will receive code 200 and you can see that you requested it, but no records were found in the database.