It is the same thing here in Calgary. If the city knows about underground storage, they will lay all kinds of "by-law" charges. Don't even get me started on all the stupid by-laws here in Calgary - it is insane!!!
You are allowed to have above ground water storage. The way that you would have to do it is have the water from your rain-gutters "filter" down to the largest barrels that you can handle. The barrels must be able to be drained from the bottom of the barrel, so, making some sort of stand would be perfect to raise it 3 to 5" above the actual ground. The next thing that you would want to do is install a overflow-valve at the top - and again - filter it.
The water will overflow to the ground - or - you can "cascade" the water to a second / third / forth barrel. Depending on how friendly you are with your neighbours, they might allow you to collect the rain-water from their houses as well. Garage? Collect there as well. Sheds? You can do it again there.
The filter is not for the water as much as keeping un-wanted bugs from making a home in that water. Window screening works very well for this. It will keep mosquitoes, wasps, bees from making a home there.
The city cannot charge you extra sewage fees for the water collected from rain.
