You don't need to call the event handler of ddlCountry, that may reset the selection in State dropdown. Further you seem to have other problems too.
You are trying to filter country by stateid.
protected void ddlState_SelectedIndexChanged(object sender, EventArgs e)
int M_STATE_SLNO = Convert.ToInt16(ddlState.SelectedValue);
SqlConnection con = new SqlConnection(strConnection);
SqlCommand cmd = new SqlCommand("select * from M_COUNTRY where M_COUNTRY_CODE=(SELECT M_COUNTRY_CODE FROM M_STATE WHERE M_STATE_CODE="+M_STATE_SLNO+")", con);
SqlDataAdapter da = new SqlDataAdapter(cmd);
DataSet ds = new DataSet();
ddlCountry.DataSource = ds;
ddlCountry.DataTextField = "M_COUNTRY_NAME";
ddlCountry.DataValueField = "M_COUNTRY_CODE";
Hope, it helps :)