Old post but as it comes up for what I was searching for I thought I'd add some information to this topic. I was going to add a comment but I don't have enough rep.
As others have said:
connection.ConnectionTimeout is used for the initial connection
command.CommandTimeout is used for individual searches, updates, etc.
But:
connection.ConnectionTimeout is also used for committing and rolling back transactions.
Yes, this is an absolutely insane design decision.
So, if you are running into a timeout on commit or rollback you'll need to increase this value through the connection string.