Umm, write offs are for taxpayers, not tax collectors.
There are a couple of reasons the State leases office space versus building their own. First and foremost, this is a state inhabited by mostly Republicans. Republicans as a general rule, want to contract out as much of government functions as possible. In this example, they would prefer to see a private enterprise make a buck out of renting to the state.
Secondly, and somewhat irrespective of the above, renting allows the State to be more nimble (well, as nimble as government can be) when it comes to a changing workforce. If you build, that's a long-term commitment and comes with risk, both natural and economic. Thus, the State can always pull out and go a cheaper route at the end of the rental term.