check and uncheck RadioButton

I will suggest you to use Checkbox control where you can actually do what you have asked.
But radio button is only that you want to use refer following code :

bool blnState;

public Form1()
{
    InitializeComponent();
}

private void radioButton1_MouseDown(object sender, MouseEventArgs e)
{
    blnState = radioButton1.Checked;
}

private void radioButton1_MouseUp(object sender, MouseEventArgs e)
{
    radioButton1.Checked = !blnState;
}

where radioButton1 is the name of the radio button that you are using.
I have used the mousedown and mouseup events of this control.