This invention provides a threaded connection for pipe or tube that has a non-sticky surface and that suppresses the occurrence of rust and exhibits excellent galling resistance and airtightness even in an extremely low temperature environment without using compound grease, a method of producing the same, and a composition for forming a solid lubricating coating on the threaded connection. A solid lubricating coating (24) formed from a composition containing a binder, a fluorine addition agent, a solid lubricant and a rust proof addition agent is coated as a topmost surface treatment coating on a contact surface of at least one of a pin and a box. Even when exposed to an extremely low temperature environment, the solid lubricating coating (24) can maintain adhesiveness and exhibit a lubricating function, can suppress the occurrence of galling of a threaded connection, and can also secure airtightness after fastening.