This seems to be a fairly common variant of the "brainless beauty" trope.
We, the audience know that the word is 'arraigned' but by having her mouth it as 'arranged', it conveys to the audience that while Madeline may be loyal, resourceful and clearly besotted with Dixon Hill, she's not the brightest bulb on the porch.
There's another variation of this joke in TNG: Clues
MADELINE: Doesn't matter if you're from the moon, Hon. Mister Hill is incommuni... incommunica...
MADELINE: That's it. Sorry, Hon.
The original screen direction for her in TNG: The Big Goodbye was that she was a
a plain blond with a bubbly personality
which does seems like Hollywood code.
On a related note (and apropos of nothing) you may find it interesting that she was entirely absent in the scene as originally written. Dix enters the bar and speaks to Rex but Madeline was nowhere to be seen.