How do I behave my application's logged in same as asp.net logged in

You can add a custom Role Provider class inherited from RoleProvider and override the functions. After adding the class, change your default provider name in the web config

For Example:
Add a class named CustomRoleProvider to you Appcode folder

using System;
using System.Collections.Specialized;
using System.Web.Security;

namespace TestApp.AppCode
{
public class CustomRoleProvider : RoleProvider
{

public override string ApplicationName { get; set; }



public override void Initialize(string name, NameValueCollection config)
{
base.Initialize(name, config);

}
public override bool IsUserInRole(string username, string roleName)
{
string[] roles = GetRolesForUser(username);
foreach (string role in roles)
{
if (role.Equals(roleName, StringComparison.OrdinalIgnoreCase))
{
return true;
}
}
return false;
}

public override string[] GetRolesForUser(string username)
{
//Add code to get user roles
}

public override void AddUsersToRoles(string[] usernames, string[] roleNames){

}

public override void CreateRole(string roleName) { }
public override bool DeleteRole(string roleName, bool throwOnPopulatedRole) { return false; }
public override string[] FindUsersInRole(string roleName, string usernameToMatch) { return null; }
public override string[] GetAllRoles() { return null; }
public override string[] GetUsersInRole(string roleName) { return null; }
public override void RemoveUsersFromRoles(string[] usernames, string[] roleNames) { }
public override bool RoleExists(string roleName) { return false; }

}
}
}

Change your web config role provider

<roleManager enabled="true" defaultProvider="CustomRoleProvider" >
     <providers>
       <clear/>
       <add name="CustomRoleProvider" type="TestApp.AppCode.CustomRoleProvider"/>
     </providers>
   </roleManager>