Do I need to complete a law library registration?

It depends on where you live and where you work.

If you live in Douglas County, but your office is elsewhere in Kansas, then you do not need to complete the registration.
If you live in Douglas County, but your office is in another state, then you do need to complete the registration.
If you do not live in Douglas County, but your office is in Douglas County, then you do need to complete the registration.

K.S.A. 20-3126(e) states: “For the purposes of this section, an attorney shall be required to be registered in the county: (1) Where the attorney's principal office is located, if such attorney is a resident of Kansas or a resident of another state; or (2) where the attorney resides, if such attorney's principal office is located in another state. The principal office shall be the principal office of the attorney and not the principal office of such attorney's firm.”