source: Common/SplitButton.cs

using System.ComponentModel;
using System.Drawing;
using System.Windows.Forms;

namespace Common
{
    public class SplitButton : Button
    {
        [DefaultValue(null)]
        public ContextMenuStrip Menu { get; set; }

        [DefaultValue(false)]
        public bool ShowMenuUnderCursor { get; set; }

        private bool menuShown = false;

        protected override void OnMouseDown(MouseEventArgs mouseEvent)
        {
            if (mouseEvent.X < ClientRectangle.Width - (int) DpiScaling.Scale(20))
            {
                base.OnMouseDown(mouseEvent);
            } else
            if (Menu != null && mouseEvent.Button == MouseButtons.Left)
            {
                Point menuLocation;

                if (ShowMenuUnderCursor)
                {
                    menuLocation = mouseEvent.Location;
                }
                else
                {
                    menuLocation = new Point(0, Height);
                }

                if (!menuShown)
                {
                    menuShown = true;
                    Menu.Show(this, menuLocation);
                }
                else
                {
                    menuShown = false;
                    Menu.Hide();
                }
                
            }
        }

        protected override void OnPaint(PaintEventArgs pevent)
        {
            base.OnPaint(pevent);

            if (Menu == null) return;
            int arrowX = ClientRectangle.Width - (int)DpiScaling.Scale(14);
            int arrowY = ClientRectangle.Height / 2 - 1;

            Brush brush = Enabled ? SystemBrushes.ControlText : SystemBrushes.ControlDark;
            Point[] arrows = new Point[] { 
                new Point(arrowX, arrowY), 
                new Point(arrowX + (int)DpiScaling.Scale(8), arrowY), 
                new Point(arrowX + (int)DpiScaling.Scale(4), arrowY + (int)DpiScaling.Scale(4))
            };
            pevent.Graphics.FillPolygon(brush, arrows);
        }
    }
}