At the compqny I used to work for, all employees are supposed to sign a 12 month contract, but it seemed like with every other person, they'd forget to give them the contract. In those cases, the pilots just simply didnt sign, and they got off on never having to deal with the contract. Of course when it came time to upgrade or do a recurrent, they'd make sure to offer them the contract BEFORE doing the training.
My advice is to simply ignore the request to sign the contract. Only sign it if they really start to threaten you with termination over it (which would be a really dumb move on their part.)