THE City Hall Public Library is joining the two Urban Council public libraries at Lai Chi Kok and Electric Road in a re-registration exercise for readers. New library cards will be issued to readers at these libraries in connection with the computerisation of the libraries, which will be operational in phases from April. ''The re-registration exercise will be joined by Tsz Wan Shan Public Library from Monday, and the rest of the 31 public libraries within the next five months,'' said an Urban Services Department spokesman. ''Those under the age of 18 will need to have the application forms signed by a parent or a guardian and produce photocopies of their identification papers.'' Readers issued with the new cards will be able to enjoy a faster and more convenient service when the system is fully implemented in mid-1995.