In his new "The Phone Book: The Curious History of the Book That Everyone Uses But No One Reads," historian Ammon Shea writes that for a few decades at the end of the 19th century and start of the 20th, there was a hand-lettered Chinese phone book in San Francisco. This was for Chinese customers of Pacific Bell who used the only foreign-language phone exchange in the country.
Chinatown's first phone, in a Bush Street office, was in operation in the 1880s, and was much used by "farmers selling produce or looking for laborers." Beginning in 1890, residents had access to a public phone in the offices of a Chinese-language newspaper. By 1894, a Chinatown switchboard linked 37 phones; in 1898, they became part of Pacific Telephone and Telegraph.
Because Chinese characters are based on ideas rather than letters, the "directory" system was not alphabetic, and most operators would spend a great deal of their first months on the job trying to memorize phone numbers.
While Santa Cruz may not have such a distinctive history of telephone directories our Special Collections Department does have a small collection of phone directories from as far back as 1918. The collection is in NRLF and more details about its scope can be found here.
Other historical directories more readily available include Polk and Haines directories which can be found in Cruzcat. A detailed list of historical collections of local telephone directories held in various repositories throughout the county can be found on page 65 of Every Structure Tells a Story: How to Research the History of a Property in Santa Cruz County.