In order to answer your question, let us take a look at the definition of crime and then see how the character of Dinah Brand can shed light upon it. The definition of crime is as follows:
an action or an instance of negligence that is deemed injurious to the public welfare or morals or to the interests of the state and that is legally prohibited.
Despite the fact that I find this particular definition of crime incredibly interesting (especially in the idea of being “injurious to the … morals”), the connection to Dinah Brand can be noticeable immediately (and especially within the third chapter that his named after her).
In further investigation of Dinah Brand, one must realize that this story continues mostly through dialogue of the corrupt characters who are all trying to confound each other. This makes it even harder to figure out the motives of each character. If we look at some of this dialogue, we can see how her actions fit the definition of crime above. The single most telling piece of information about Dinah is given by the chief of police:
[Dinah Brand is a] soiled dove, as the fellow says, a deluxe hustler, a big league gold-digger.
As readers, we learn this even before meeting Dinah. Here we can see that Dinah is already “injurious to the public welfare” by being a “hustler” as well as someone only interested in money. Dinah, however, only loosely fits into the first murder in the story because she is implicated as having an affair with Donald Wilson.
In regards to being “injurious to the … morals” of the town, Dinah can be seen as a “hustler” once again by becoming the Op’s closest ally and possible romantic partner, supposedly all for money. The irony is that she, herself, is manipulated by the Op as everyone in Personville/Poisonville gets corrupted. Eventually, Dinah Brand condemns herself in regards to crime and greed:
“If you talked my language,” she drawled, looking narrow-eyed at me, “I might be able to give you some help.”
“Maybe if I knew what it was.”
“Money,” she explained, “the more the better I like it.”
Quite simply, Dinah Brand will do anything for money. It doesn’t matter whether action or omission is “legally prohibited,” as in the definition of crime.
In conclusion, it is important to realize that there are a huge number of characters in this work of literature. The reason is simple: the author is trying to show the widespread corruption of greed in America. Dinah Brand is simply one of these characters who participate in corruption through greed.