After murdering an immigrant, he convinces his psychiatrist to declare him insane so as not to be put on trial, but a detective will follow his steps to lock him up.

As the others have pointed out, best you focus on one main character and change the premise so it makes logical sense in the current legal system.

Also, I suggest you check out the 'Formula' tab on the top bar to learn more about logline basics.

Unfortunately, the premise is flawed.? Being declared insane won't get him off the legal hook.? ?He? will still be arrested. tried and convicted.? That's the way it works.? All that being declared insane might do is mitigate his sentence.? He might get a life sentence instead of the death penalty.

Maybe somewhere along -- "When his wife's therapist pleads insane after killing her, a grieving detective must prove it otherwise and bring justice" (to make things personal for him...)