[c#] Error "There is already an open DataReader associated with this Command which must be closed first" when using 2 distinct commands

Try to combine the query, it will run much faster than executing an additional query per row. Ik don't like the string[] you're using, i would create a class for holding the information.

    public List<string[]> get_dados_historico_verificacao_email_WEB(string email)
    {
        List<string[]> historicos = new List<string[]>();

        using (SqlConnection conexao = new SqlConnection("ConnectionString"))
        {
            string sql =
                @"SELECT    *, 
                            (   SELECT      COUNT(e.cd_historico_verificacao_email) 
                                FROM        emails_lidos e 
                                WHERE       e.cd_historico_verificacao_email = a.nm_email ) QT
                  FROM      historico_verificacao_email a
                  WHERE     nm_email = @email
                  ORDER BY  dt_verificacao_email DESC, 
                            hr_verificacao_email DESC";

            using (SqlCommand com = new SqlCommand(sql, conexao))
            {
                com.Parameters.Add("email", SqlDbType.VarChar).Value = email;

                SqlDataReader dr = com.ExecuteReader();

                while (dr.Read())
                {
                    string[] dados_historico = new string[6];
                    dados_historico[0] = dr["nm_email"].ToString();
                    dados_historico[1] = dr["dt_verificacao_email"].ToString();
                    dados_historico[1] = dados_historico[1].Substring(0, 10);
                    //System.Windows.Forms.MessageBox.Show(dados_historico[1]);
                    dados_historico[2] = dr["hr_verificacao_email"].ToString();
                    dados_historico[3] = dr["ds_tipo_verificacao"].ToString();
                    dados_historico[4] = dr["QT"].ToString();
                    dados_historico[5] = dr["cd_login_usuario"].ToString();

                    historicos.Add(dados_historico);
                }
            }
        }
        return historicos;
    }

Untested, but maybee gives some idea.