Step1: Import the MessageUI using :- import MessageUI

Step 2: class ViewController: UIViewController, MFMessageComposeViewControllerDelegate

Step 3: when you tap on the button the list of contact will appear and you can choose the contact from the list

@IBAction func btnShowContactClicked(sender:UIButton)
        {
        println("btn clicked")
            var messageVC = MFMessageComposeViewController()
            messageVC.body = "Enter a message";
            messageVC.recipients = ["Enter tel-nr"]
            messageVC.messageComposeDelegate = self;

            self.presentViewController(messageVC, animated: false, completion: nil)
        }

        func messageComposeViewController(controller: MFMessageComposeViewController!, didFinishWithResult result: MessageComposeResult) {
            switch (result.value) {
            case MessageComposeResultCancelled.value:
                println("Message was cancelled")
                self.dismissViewControllerAnimated(true, completion: nil)
            case MessageComposeResultFailed.value:
                println("Message failed")
                self.dismissViewControllerAnimated(true, completion: nil)
            case MessageComposeResultSent.value:
                println("Message was sent")
                self.dismissViewControllerAnimated(true, completion: nil)
            default:
                break;
            }
        }