textbox with dropdownlist on mouse over

Hi,
why don't you use comboBox for this type of situation.
try this one,

take a comboBox control, write the following code under the MouseEnter event and MouseLeave events of comboBox.

private void comboBox1_MouseEnter(object sender, EventArgs e)
        {
            this.comboBox1.DropDownStyle = System.Windows.Forms.ComboBoxStyle.DropDown;
        }

        private void comboBox1_MouseLeave(object sender, EventArgs e)
        {
            this.comboBox1.DropDownStyle = System.Windows.Forms.ComboBoxStyle.Simple;
        }

And also write the following code under the Form Load event

private void Form1_Load(object sender, EventArgs e)
        {
            this.comboBox1.DropDownStyle = System.Windows.Forms.ComboBoxStyle.Simple;
        }

I hope this helps to you.