First try to connect to the SQL Server without providing any database name,or path just like below:

ConnectionString = @"Data Source= YourDataSource ;Integrated Security=True;Connect Timeout=30";

Note:
YourDataSource can either be . or .\SQLEXPRESS or .\MSSQLSERVER or (local)\SQLEXPRESS or (localdb)\v11.0 or etc.

Then by using the following query, detach your database.

"ALTER DATABASE [your DB] SET OFFLINE WITH ROLLBACK IMMEDIATE \n\r exec sp_detach_db @dbname = [your DB]";

Ok.

My Sample code:

sql_connect1.ConnectionString = @"Data Source=.\sqlexpress;Integrated Security=True;Connect Timeout=30";
sql_command.CommandText = "ALTER DATABASE [IRAN] SET OFFLINE WITH ROLLBACK IMMEDIATE \n\r exec sp_detach_db @dbname = [IRAN]";
                  sql_command.Connection = sql_connect1;
                  sql_connect1.Open();
                  sql_command.ExecuteNonQuery();
                  sql_connect1.Close(); 

you can detach a database on SqlServer by the following code: There is a stored procedure in SqlServedr 'sp_detach_db' for detach a database, has one argument DataBaseName. Here in the code 'MyDatabase' is the database name you should change it with your database name

// C# Code

SqlConnection conn = new SqlConnection("Server=(local); Data Source=;Integrated Security=SSPI");
SqlCommand cmd = new SqlCommand("", conn);

cmd.CommandText = "sys.sp_detach_db MyDatabase";

conn.Open();

cmd.ExecuteNonQuery();

cmd.Dispose();
conn.Dispose();

You can use stored procedures for your problem. following link can be useful:

http://msdn.microsoft.com/en-us/library/aa259611.aspx

Myo Thu's comments lead me in the right direction, so here's a summary of steps on how to detach the database.

Step 1: Reference the following DLL's in your project [Reference]:

Microsoft.SqlServer.ConnectionInfo.dll

Microsoft.SqlServer.Smo.dll

Microsoft.SqlServer.Management.Sdk.Sfc.dll

Microsoft.SqlServer.SqlEnum.dll

Step 2: using:

using Microsoft.SqlServer.Management.Smo;
using Microsoft.SqlServer.Management.Common;

Step 3: Code

var server = new Server(new ServerConnection(@"MyMachine\SQL2012"));
// Ensure database is not in use
server.KillAllProcesses("TestDatabase");
server.DetachDatabase("TestDatabase", true);

EDIT: Now documented in my blog here