const inputRef = React.createRef();

const menu = (
  <div style={{ padding: 16, background: '#FFF', border: '1px solid red' }}>
    <Input ref={inputRef} />
  </div>
);

ReactDOM.render(
  <Dropdown
    overlay={menu}
    trigger={['click']}
    onVisibleChange={visible => {
      if (visible) {
        setTimeout(() => inputRef.current.select());
      }
    }}
  >
    <a className="ant-dropdown-link" href="#">
      Click me <Down />
    </a>
  </Dropdown>,
  mountNode,
);