Hmmm, looks like opposite compound leaves so I think ash is a good bet. There are just a few tree species that have opposite branching - Maple, Ash, Dogwood (aka "MAD") and maple and dogwood have simple leaves. The pattern in the bark looks ashy to me, too.  Like crisscrossing A's or X's.  Hopefully the damage to their house wasn't too severe. 

If you are just wondering if it is an Ash tree vs some other type like hickory etc.  I would say it is an Ash tree.  Why?  The bark has a diamond pattern which is typical of Ash.  The leaves are compound (see below) and appear more ash like then hickory which also has a compound leaf.

If you are wondering about what type of Ash tree.  I am not sure about that.  It is not real clear based on comparing information on different Ash species whether it is White, or Green Ash which are the common species planted.  

The leaflets (form a compound leaf) https://ipm.ucanr.edu/TOOLS/TURF/PESTS/broadsimcom.html and on White ash the underside of the leaflets is more whitish colored and they have a longer leaflet stem where they attach to the main leaf stalk than Green Ash.

For the above reasons I would say this is more likely a White Ash.

If others have good input to key this out to a specific type of Ash please share.

It's hard to know tree species for sure with many suburban trees. If they're planted by homeowners they could be from anywhere in the world, which opens up species possibilities far beyond what you'd typically see in New York. Assuming it's a native tree then I agree that it's mostly likely a white ash, based on the stalked leaflets and the opposite branching pattern.