When Dorinda Dances — Brett Halliday

To save a judge's daughter, Mike Shayne must invade the red-light district
 
For twenty years, Judge Nigel Lansdowne has been one of Washington's greatest progressives. The red-baiters in Congress would do anything to destroy his reputation, and they may have found the perfect weapon. Her name is Julia, but when she dances she goes by Dorinda. The judge's daughter came to Miami in search of a new life, and she found it dancing nude in the city's infamous red-light district. Mike Shayne is hired to bring Julia home before the judge's enemies learn of her new career, but his real job will be keeping her alive.
 
Someone in Miami wants this beautiful dancer dead, and only Mike Shayne can help her. In the nightclubs of Miami Beach, music is played to a deadly beat.

When Dorinda Dances is the 20th book in the Mike Shayne Mysteries, but you may enjoy reading the series in any order.