Old Old Sci-Fi Book possilbly one of the clic writers?

I'm looking for a very old book I read when I was reading the masters, Asimov, Bradbury, etc. It had to do with the human race being discovered and brought into a federation of Sentients. We had to be sponsored by another of the "recognized" advanced sentient Species. I don't remember if the main character was a detective or an investigator of some kind. I remember one character that stood out, from a race of tree like beings, being described as looking like a huge stalk of broccoli, with whom the main character met several times in the book, mostly while on a spaceship crossing the galaxy doing his investigation. Any one know what the title is?