コンボボックスの選択値を変えるごとにDataGridViewで表示するデータを変更するにはDataViewを使用するのが便利かと思います。 DataTableなどにも一致する行を取得するメソッドがありますが、こちらのほうが便利かと思います。

C#

    public partial class Form2 : Form
    {
        DataTable dt = new DataTable();
        DataTable dt2 = new DataTable();
        public Form2()
        {
            InitializeComponent();
        }
        private void Form2_Load(object sender, EventArgs e)
        {
            SqlConnectionStringBuilder connBldr = new SqlConnectionStringBuilder();
            connBldr.DataSource = @".\SQLExpress";
            connBldr.InitialCatalog = "pubs";
            connBldr.IntegratedSecurity = true;
            SqlConnection conn = new SqlConnection(connBldr.ConnectionString);
            SqlCommand cmd = new SqlCommand();
            cmd.Connection = conn;
            cmd.CommandText = "SELECT minit FROM employee GROUP BY minit ORDER BY minit";
            SqlDataAdapter sda = new SqlDataAdapter();
            sda.SelectCommand = cmd;
            //コンボボックス用のデータを取得
            sda.Fill(dt);
            //DataGridViewのデータを取得
            cmd.CommandText = "SELECT * FROM employee";
            sda.Fill(dt2);
            //次を設定しないと表示がおかしくなります。
            comboBox1.DisplayMember = "minit";
            comboBox1.ValueMember = "minit";
            comboBox1.DataSource = dt;
            dataGridView1.DataSource = dt2;
        }
        private void comboBox1_SelectedIndexChanged(object sender, EventArgs e)
        {
            DataView dv = dt2.DefaultView;
            //ここでフィルターを設定します。
            dv.RowFilter = "minit = '" + this.comboBox1.SelectedValue.ToString() + "'";
        }
    }

VB.NET

Imports System.Data.SqlClient
Imports System.Data
Public Class Form1
    Dim dt As DataTable = New DataTable()
    Dim dt2 As DataTable = New DataTable()
    Private Sub Form1_Load(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles MyBase.Load
        Dim connBldr As SqlConnectionStringBuilder = New SqlConnectionStringBuilder()
        connBldr.DataSource = "."
        connBldr.InitialCatalog = "pubs"
        connBldr.IntegratedSecurity = True
        Dim conn As SqlConnection = New SqlConnection(connBldr.ConnectionString)
        Dim cmd As SqlCommand = New SqlCommand()
        cmd.Connection = conn
        cmd.CommandText = "SELECT minit FROM employee GROUP BY minit ORDER BY minit"
        Dim sda As SqlDataAdapter = New SqlDataAdapter()
        sda.SelectCommand = cmd
        'コンボボックス用のデータを取得
        sda.Fill(dt)
        'DataGridViewのデータを取得
        cmd.CommandText = "SELECT * FROM employee"
        sda.Fill(dt2)
        '次を設定しないと表示がおかしくなります。
        Me.ComboBox1.DisplayMember = "minit"
        Me.ComboBox1.ValueMember = "minit"
        Me.ComboBox1.DataSource = dt
        Me.DataGridView1.DataSource = dt
    End Sub
    Private Sub ComboBox1_SelectedIndexChanged(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles ComboBox1.SelectedIndexChanged
        Dim dv As DataView = dt2.DefaultView
        'ここでフィルターを設定します。
        dv.RowFilter = "minit = '" & Me.ComboBox1.SelectedValue.ToString() & "'"
    End Sub
End Class