Looking for an book I believe to be in Urban fantasy. It has a female private detective/ investigator that was called in on a murder. I remember the first part of the book, where the victim was suspended[?] in a gazebo [basically displayed for maximum shock value]. There were also reports of dog attacks in the news. But the supernatural agency she reports to claims they are death hounds or something like that. This is part of a series and this isn't the first book.

Haven't read them myself, but maybe you're looking for the Dresden Files? There is a character (Karrin Murphy) who is a detective/police officer that deals with unusual crime scenes:
...Murphy is introduced as an officer who works within the Special Investigations (SI) division of the Chicago Police Department, which handles cases in which something unexplainable or supernatural is involved...
The Dresden Files - Wikipedia, the free encyclopedia

No. Not that series.