Make Client Server Without Installing Sql Server?

I have an application in which i have a database .mdf file in directory which i use a connection string to give a path of to access it, which means without installing sql server i can access database. Connection string below to access this database(.mdf) which placed in the directory.

dim con as sqlconnection = New SqlConnection("Data Source=.SQLExpress;integrated security=true;attachdbfilename=|DataDirectory|Universal_data.mdf;user instance=true")

Now the question is that if i access this .mdf file without installing sql server, i also want to access to this .mdf file on other computer(client) after creating DSN or any other connectivity tool.

Let me know you that when i install sql server 2000 or 2005 i create SA user name and password which i use to create DSN on client computer and give SA username and password in the connection string that successfully works and client get access to sql server, connection string is below.

Dim serv = "MY-LAPTOP"
dim con as sqlconnection = new sqlconnection("Data Source=" & serv & ";Initial Catalog=clinic;Persist Security Info=True;User ID=sa")

I only need to know that my application access .mdf file without installing sql server works fine on a single computer, and i want to give access to this .mdf file on other clients without installing sql server on server computer (like i mentioned above paragraph) how will do it.....