A party is entitled to propound written discovery in an unlawful detainer case, just like any civil litigation matter. The only difference is that the responses are due in 5 days instead of 30 days. For starters, one can send the Judicial Council Form Interrogatories - Unlawful Detainer. These "check the box" questions cover all of the most commonly encountered issues and defenses in an eviction case.
For the Judicial Council Form Interrogatories, see the link below.
In addition to Form Interrogatories, any of the other types of written discovery are also permissible. These include Special Interrogatories, Request for Admissions and Demand for Production of Documents. Unfortunately, however, each of these must be specially prepared because there are no Judicial Council preprinted forms.
Get a good guide, like the one linked below, written for landlords on the UD process, to see how it works.
I'm only licensed in CA. Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.