This morning I didn’t have internet access and was trying to find this in my notes (which are also my blog posts), and I couldn’t; so purely for my own benefit, the following is a method of handling touch or mouse input in Monogame:

        public void HandleInput()
        {
            ProcessMouseInput();
            ProcessTouchInput();
            ProcessKeyboardInput();
        }

        private void ProcessMouseInput()
        {
            var currentMouse = Microsoft.Xna.Framework.Input.Mouse.GetState();

            if (currentMouse.LeftButton == Microsoft.Xna.Framework.Input.ButtonState.Pressed)
            {
                HandlePressed(currentMouse.Position, _controlledObject);
            }
        }

        private void ProcessTouchInput()
        {
            var currentTouch = Microsoft.Xna.Framework.Input.Touch.TouchPanel.GetState();

            foreach (var touch in currentTouch.Where(t => t.State == Microsoft.Xna.Framework.Input.Touch.TouchLocationState.Pressed))
            {
                HandlePressed(touch.Position, _controlledObject);
            }


        }

        private void ProcessKeyboardInput()
        {
            var currentKeys = Microsoft.Xna.Framework.Input.Keyboard.GetState();
            if (currentKeys.IsKeyDown(Microsoft.Xna.Framework.Input.Keys.Left))
            {
                _handler.GoLeft(_controlledObject);

By changing Pressed to Released, you can detect when the mouse button click / touch finished; however, if you hold your finger / mouse button down, it will only return a single result.