downloaded Sql server management 2008 r2 and got it installed. Its getting installed but when I try to connect it via .\SQLEXPRESS it shows error. DO I need to install any SQL service on my system?
You installed management studio which is just a management interface to SQL Server. If you didn't (which is what it seems like) already have SQL Server installed, you'll need to install it in order to have it on your system and use it.
http://www.microsoft.com/en-us/download/details.aspx?id=1695