how to check if user is login or not in community site..

This should be what you need:

<#if user.anonymous == true>
	<!-- user is not logged in -->
<#else>
	<!-- user is logged in -->
</#if>

 You can see what other freemarker context objects are available here: http://lithosphere.lithium.com/t5/developers-knowledge-base/user-FreeMarker-context-object/ta-p/9339