I am not entire sure what you mean by "Segue to other storyboard"? The following code allows you to jump to a totally different view controller tree inside the same storyboard by a click of button or other action.
AppDelegate *delegate = (AppDelegate *)[[UIApplication sharedApplication] delegate];
UIStoryboard *storyboard = [UIStoryboard storyboardWithName:@"Main" bundle:nil];
UIViewController *initViewController = [storyboard instantiateViewControllerWithIdentifier:@"SecondScreen"];
delegate.window = [[UIWindow alloc] initWithFrame:[[UIScreen mainScreen] bounds]];
delegate.window.rootViewController = initViewController;
[delegate.window makeKeyAndVisible];
Main is the name of your storyboard that you want to jump into.
SecondScreen is the storyboard ID of the view controller. Most likely it is a navigation or a container. You will need to set "SecondScreen" under identity inspector.