How to set cornerRadius for only top-left and top-right corner of a UIView?

I am not sure why your solution did not work but the following code is working for me. Create a bezier mask and apply it to your view. In my code below I was rounding the bottom corners of the _backgroundView with a radius of 3 pixels. self is a custom UITableViewCell:

UIBezierPath *maskPath = [UIBezierPath
    bezierPathWithRoundedRect:self.backgroundImageView.bounds
    byRoundingCorners:(UIRectCornerBottomLeft | UIRectCornerBottomRight)
    cornerRadii:CGSizeMake(20, 20)
];

CAShapeLayer *maskLayer = [CAShapeLayer layer];

maskLayer.frame = self.bounds;
maskLayer.path = maskPath.CGPath;

self.backgroundImageView.layer.mask = maskLayer;

Swift version with some improvements:

let path = UIBezierPath(roundedRect:viewToRound.bounds, byRoundingCorners:[.TopRight, .BottomLeft], cornerRadii: CGSizeMake(20, 20))
let maskLayer = CAShapeLayer()

maskLayer.path = path.CGPath
viewToRound.layer.mask = maskLayer

Swift 3.0 version:

let path = UIBezierPath(roundedRect:viewToRound.bounds,
                        byRoundingCorners:[.topRight, .bottomLeft],
                        cornerRadii: CGSize(width: 20, height:  20))

let maskLayer = CAShapeLayer()

maskLayer.path = path.cgPath
viewToRound.layer.mask = maskLayer

Swift extension here

Pay attention to the fact that if you have layout constraints attached to it, you must refresh this as follows in your UIView subclass:

override func layoutSubviews() {
    super.layoutSubviews()
    roundCorners(corners: [.topLeft, .topRight], radius: 3.0)
}

If you don't do that it won't show up.

And to round corners, use the extension:

extension UIView {
   func roundCorners(corners: UIRectCorner, radius: CGFloat) {
        let path = UIBezierPath(roundedRect: bounds, byRoundingCorners: corners, cornerRadii: CGSize(width: radius, height: radius))
        let mask = CAShapeLayer()
        mask.path = path.cgPath
        layer.mask = mask
    }
}

Additional view controller case: Whether you can't or wouldn't want to subclass a view, you can still round a view. Do it from its view controller by overriding the viewWillLayoutSubviews() function, as follows:

class MyVC: UIViewController {
    /// The view to round the top-left and top-right hand corners
    let theView: UIView = {
        let v = UIView(frame: CGRect(x: 10, y: 10, width: 200, height: 200))
        v.backgroundColor = .red
        return v
    }()
    
    override func loadView() {
        super.loadView()
        view.addSubview(theView)
    }
    
    override func viewWillLayoutSubviews() {
        super.viewWillLayoutSubviews()

        // Call the roundCorners() func right there.
        theView.roundCorners(corners: [.topLeft, .topRight], radius: 30)
    }
}