Done: Groucho Marx, Master Detective by Ron Goulart, 1998, 031218106X.
I ran across a reference to this on a forgotten books comment. Cannot recall what other book was being discussed. I figured to try this out. This was well done but Groucho is a main character and I kept wondering if Goulart was writing new jokes or using old ones that Groucho used.
Scriptwriter Frank Denby used to be a police reporter for a few Los Angeles newspapers. Come 1937 he is a writer for Groucho's soon-to-premier radio show. On his way to a meeting with network executives Denby's car is run into by a woman on a bicycle when he stops for traffic. Denby is smitten with Jane, drives her and her wrecked bicycle home, and heads to his meeting. Groucho is introduced. Groucho cracks jokes.
Turns out the traffic jam that resulted in Denby meeting Jane was rubbernecking at a crime scene. An actress committed suicide. Groucho used to bang the actress. Groucho was still fond of her and does not believe the suicide report. Groucho asks Denby to help investigate. Denby uses his old police and newspaper contacts. Groucho acts silly.
Dead Girl looks to have been beaten to death. Her place was ransacked. She bragged about signing a multi-year studio contract. Groucho is upset. Groucho still cracks jokes. Croucho and Denby sleuth. Denby and Jane do the dirty deed. Groucho and Denby find suspects. Someone is trying to kill Groucho.
More things happen. Hollywood happenings with big-name stars of the time. Fans love to meet Groucho. Groucho cannot resist telling jokes and pulling their legs (not literally, he's not Harpo). Another murder attempt on Groucho. More sex with Denby and Jane. More suspects and sleuthing. Groucho and Denby solve the crime and Denby and Jane escape a nasty murder attempt. The bad guys get a public comeuppance via very public handgun action. Groucho cracks jokes.
1. Old cars.
2. Many Marx monkeyshines.
3. Several people speak to Groucho throughout the novel expressing how sorry they are his and the Marx Brothers movie careers are washed up.