Unless you're a police officer with access at the department, I wouldn't count on getting a rap sheet freely. Rap sheet (Records of Arrest and Prosecution) is a report/print out of a person's history withing the police departments' databases, either shared or not. You can compile your own information of past records of prosecution by looking up criminal court records, which are free by linking to the Iowa Court Records link on this page under Iowa Free Public Records Directory above. That is a free search directly from Iowa's courts. From there you can go fishing around for other free records, since you're trying to avoid having to pay, you will need to dig up many of the free databases. Arrests can be viewed from individual county webpages, usually from their law enforcement, which will provide jail and arrest lists. There are many other similar examples.
You can go to the court directly and view documents, or request them for a nominal fee by the records division of that courthouse. The state of Iowa also offers an open/free online case search. To get to that webpage, click on the link above "Iowa Court Records", that will land you on the state's court webpage, then click on "Start A Case Search Here!".
The County Recorder's office from county divorce was issued should be able to provide this- there may be a fee for copy
Which county is the case in? Civil and criminal courts have calendars posted online.
Arrest records generally come from the arresting police agency which is usually the sheriff or local police department, state troopers do not make the majority of the arrests. Unless you’re an active member law enforcement, access to the database which houses all arrest information is restricted. An arrest report is different from a computer generated rap sheet. It is in detail, similar to a field report or incident report which you can request from the department directly. Individual department in Iowa have websites with information about providing the public with arrest reports. In some cases the fee is waived if you are a qualifying party to the case related to the arrest. Be aware of requesting arrest records coming from the state, or anywhere, as they are often mislabeled as background checks. A background shows a history of convictions, crimes committed as opposed to arrests which took place before going to court.
The Iowa Secretary of State offers a corporation search from their website. Once on their website, you will see a tab for 'Search Databases', in its drop down menu select Business Entities Search. You will then be asked to enter the business name or number. You can enter a partial name if you're not sure of the spelling. The results will be a list of businesses that match the entity name showing the business number, name, status and type. Once an entity is selected, you will see more information that includes registered agent or reserving party, home office, effective and expiration dates and more. Under the same tab, you will be able to search for UCC filings, liens, land patent and more.