Detective story where a loophole in the US extradition law is used to avoid trial

Question

I read a detective story when I was a kid but can't find I now.

The protagonist confessed to a murder he didn't commit to protect a client of his detective agency (who did). However, he carefully planned his arrest and confession ahead and used a legal loophole which let him avoid standing trial, so he had to be released.

• The loophole had something to do with the extradition laws between two different US states (I think they were Nevada and Utah).
• The protagonist was arrested for something else than the murder.
• The protagonist had the sheriff drag him into the police car kicking and screaming and then used this fact when making his case.

The rest of the details I remember:

• It was (I think) an English-language story, I read it in Russian translation.
• It was set in the US, first part of the XX century.
• It was (again, I think) the first part of a series.
• The protagonist was employed in a private detective agency run by a fat woman. At one point the protagonist was talking about his employer on the phone (as she listened to the conversation) and was hesitant to describe her physical appearance. She encouraged him to go ahead and just tell that she was fat.

Answer 1

I found it myself, it was "The Bigger They Come" by A. A. Fair (the pen name of Erle Stanley Gardner).

It's the first book in his series about Donald Lam and Bertha Cool.

Yes, she’s assigning a detective to work on the case — no — no, not herself... No, she doesn’t go out by herself. She’s — she’s hardly—’

Bertha Cool said, ‘Don’t be bashful. Tell her I’m fat.’

The district attorney said, ‘Your honor, we don’t need to believe his story. We can hold him for further developments. Perhaps he—?’

‘Apparently you don’t appreciate the diabolical ingenuity of the petitioner’s position,’ Judge Oliphant said. ‘He can’t be extradited from Arizona. He isn’t a fugitive from justice ― not from California at any rate. I doubt if there is enough evidence to connect him with this Kansas City crime. If there is, there will be little difficulty in finding the petitioner. He certainly is not going to leave the State of Arizona. Here he enjoys legal immunity. Elsewhere, he would not, and the perspicacity of this petitioner is such that he not only realizes that fact but will take full technical advantage of it. I even doubt if he could be extradited to Kansas City. The petitioner is discharged.’