Yes, the numbers and a date.
...How can I use the certificate number and date to help find my relative's naturalization info?
The short answer is that the certificate number will not help you or the INS to find your relative's naturalization info. However, by providing the date in your request to the INS, it will help narrow down when your relative was naturalized, since your relative would not have been naturalized before the date noted on the manifest
Have a look here at "Manifest Markings"
http://www.jewishgen.org/InfoFiles/Manifests/http://www.archives.gov/genealogy/naturalization/Not sure if one of these is your Zdenci and thus this is where you need help from Croatia's board regulars.
http://www.familysearch.org/eng/library/fhlcatalog/supermain...=