Developers build programs based on software libraries to reduce coding effort. If a program inappropriately invokes an API parameter, the program may exhibit unexpected runtime behaviors. To help developers correctly use library APIs, researchers built tools to mine API parameter rules. However, some fundamental questions are still unexplored. For instance, what are the parameter rules overlooked by existing work, and how can we automatically extract such rules? In this paper, we conducted a large-scale empirical study to investigate the above-mentioned questions. Specifically, to study as many parameter rules as possible, we took a hybrid approach that combines automatic localization of constrained parameters with manual inspection. Our automatic approach—PARU—locates parameters that have constraints either documented in Javadoc (i.e., document rules) or implied by source code (i.e., code rules). Our manual inspection (1) identifies and categorizes rules for the located parameters, (2) analyzes how well existing tools detect the rules, and (3) identifies the mapping between document and code rules. By applying PARU to 9 widely used libraries, we located 5,334 parameters with either document or code rules. Interestingly, there are only 108 parameters that have both types of rules, and 79 of these parameters have the rules unmatched. Additionally, PARU extracted 1,688 rule-containing sentences from Javadoc and code. We manually classified these sentences into six categories, and discovered that existing techniques can reveal at most three of the categories. Our research reveals the challenges for automating parameter rule extraction, and provides insights for future tool design.