SELECT * FROM table WHERE category IN (
  SELECT category FROM (
    SELECT category, COUNT(*) AS c2 FROM (
      SELECT category, completed, COUNT(*) AS c1 FROM table
      GROUP BY category, completed
    ) AS t1
    GROUP BY category
  HAVING COUNT(*) > 1
  ) AS t2
)

B   No
C   Yes
B   No
B   Yes
C   No
C   Yes

public void Test()
{
    try
    {
        var fLayer = ArcMap.Document.Maps.get_Item(0).get_Layer(0) as IFeatureLayer;
        var categories = Categorize((ITable)fLayer.FeatureClass, "Category", "Completed");
        foreach (KeyValuePair<string, List<string>> kvp in categories)
        {
            if (kvp.Value.Count > 1)
                Debug.Print("Category {0} has {1} unique values", kvp.Key, kvp.Value.Count);
        }
    }
    catch (Exception ex)
    {
        Debug.Print(ex.Message);
    }
}

public Dictionary<string, List<string>> Categorize(ITable table, string categoryFld, string otherFld)
{
    var outList = new Dictionary<string, List<string>>();
    IQueryFilter qf = new QueryFilter();
    qf.SubFields = String.Format("{0},{1}", categoryFld, otherFld);

    int idxCat = FindField(table,categoryFld);
    int idxOther = FindField(table,otherFld);
    ICursor cur = null;
    // **edited to release cursor in a finally block**
    try
    {
        cur = table.Search(qf, true);
        IRow row;
        while ((row = cur.NextRow()) != null)
        {
            string category = GetStrVal(row, idxCat);
            string other = GetStrVal(row, idxOther);
            if (!outList.ContainsKey(category))
                outList.Add(category, new List<string>());
            if (!outList[category].Contains(other))
                outList[category].Add(other);
        }
    }
    catch
    {
        throw;
    }
    finally
    {
        System.Runtime.InteropServices.Marshal.FinalReleaseComObject(cur);
    }
    return outList;
}

public static string GetStrVal(IRow row, int idx)
{
    return row.get_Value(idx) is DBNull ? "<Null>" : row.get_Value(idx).ToString();
}

public static int FindField(ITable table, string fldName)
{
    int idx = table.FindField(fldName);
    if(idx == -1)
        throw new Exception(String.Format("field {0} not found on table {1}",
            fldName,((IDataset)table).Name));
    return idx;
}