As a contractor, assuming you're in the United States, you're relationship to this client is not the same as your relationship would be to an employer, and in most contracting relationships, you set your own hours, use your own equipment, and dictate the how part of your work.
Is it appropriate to decline overtime?
I look at this business relationship the same as I'd look at a plumber. If one of the pipes in my house were to burst on a Saturday night, most likely, If I try to call a plumber, they're either going to not answer, or they're going to want to charge me a higher fee for their services. Thus, I'd most likely just shut my water off to stop the emergency, and then wait until Monday to have the plumber come out and fix the broken pipe.
Now, if the pipe were to break in a spot where there's no emergency shutoff valve, and there's a threat of actual water damage to the expensive structure of my home, then I'd almost certainly expect to find a plumber to come out and immediately work on resolving the issue, and I'd be willing to pay the increased fees for these emergency services.
In your situation, you're working on a release, and while debatable, a release doesn't constitute an emergency, unless of course missing a deadline could create financial hardship, for instance, if we had to pay people to just stand around while waiting for the cement truck... Under normal circumstances, if resources can be reallocated, I'd expect a company to push back the release instead of calling everyone in for what isn't an emergency, financial or otherwise.
Could I get fired for this
I should also add that they could let you go if this is a blocker issue for them. That doesn't make you wrong to value your time, but it could mean you may need to clarify your availability when negotiating a contract and also do some research on whether your client would actually be a good client. You should judge and evaluate them just as diligently as they judge and evaluate you.
What a company should expect from you
To prevent problems with these expectations in the future, when meeting with a potential client, ask questions about overtime. Ask if it's expected and how often? Ask what can be done to prevent the need for overtime. Make it clear that you expect to be available outside normal business hours for emergencies, and then clearly define what is an emergency. If this isn't something you can agree on, then you or the company can politely move on with no animosity.
Contracts aren't mean to be something that you use against someone as a weapon; instead, they're designed to clarify expectations and prevent problems from escalating into a lose-lose situation for both parties, which is done by making sure the expectations of both parties are clear and that you're all on the same page.
With that said, I would hope that if the issue were a real emergency, for instance, if software you built suddenly stops working, and it's a weekend, and the client just dropped a million dollars on advertising, and the website was 404ing and not letting any of these conversions come through, then I'd expect to see you working to resolve what constitutes an expensive, detrimental leak, and putting your personal issues aside to be a team player. Hopefully, this is something that doesn't happen too often, as being a team player shouldn't mean you're a doormat. ;)
Keep in mind that the emergency scenario is just one example. As Chad mentions in the comments, another vendor or contractor dropping the ball on a deadline may have created great hardship for your client, and you may want to weigh your committment to your client against your own personal needs. Sometimes sacrifice is in order, as long as it's not constant or abusive.
Again, this information mostly applies to contractors in the United States, since that's where my experience comes from; however, New Zealand also takes a similar approach, if this applies to you.
How to handle this situation today?
Since you've already signed a contract, you'll need to discuss this issue with the client. Ideally, you should discuss this when there is no fire to put out instead of when they say they need you. My suggestion would be to bring up the issue in person, during business hours, and not by email. Email isn't really a good means of starting a discussion. There's no body language, and things you say can be misconstrued.