What could be the cause of my 2006 chrysler crossfire lets out blue smoke after sitting for a day or two

blue smoke means burning oil, either leaky piston rings or valve seats. If it doesnt do it consistantly and only for about a minute or less then just make sure your oil level is good. Repairing this is costly.

Thank you. When you say costly does that mean thousands of dollars?

yes, you would have to pull the motor and have the heads taken off and have them worked and the seats replaced, then the crank and pistons taken out to put new rings on and check your cylinder bore. You may need it bored out a little if they are out of round and oversized pistons to compensate for the new bore.