Checks to be done, before/after changing the windows login password?
Read this MSDN page for details about what to do on the SQL Server box.  This is taken from that page:

The SQL Server Database Engine and SQL Server Agent run on a computer as a service using credentials that are initially provided during setup. If the instance of SQL Server is running under a domain account and the password for that account is changed, the password used by SQL Server must be updated to the new password. If the password is not updated, SQL Server may lose access to some domain resources and if SQL Server stops, the service will not restart until the password is updated.
Change the password of the accounts used by the Database Engine and the SQL Server Agent in SQL Server 2012 by using SQL Server Configuration Manager.

If applications or other services are connecting to the SQL Server using that domain account, they will also need to know the updated password.  You may want to look at enabling logon auditing to help understand where those applications are.