If you are using Sql Server in your app, then there must be an Sql Server installation within reach of your application when it runs: that doesn't mean it must be on the same machine - that is generally a poor idea with release software for a variety of reasons - but it must be available, which normally means on the same LAN. This can be Sql Server Express or the full retail version.
If you are only using the database for single user storage, then SQLCE or SQLite are very appropriate and do not require any SQL server installation - in fact they just need a couple of assemblies which should be loaded as part of your deployment anyway. These would require changes to your code (but probably not major changes) and provided you don't want to share the DB data, they are both an excellent way to do it.
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c# application without installing MS-SQL Server in client machine[
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