My wife and I reside year-round in CA. We
>own a house that she inherited from her father
>in NH and pays property tax on it (it is not a
>rental property). Can the property tax we pay
>on the NH house be deducted on the federal
>and/or CA returns? Would there be any point
>in completing a NH tax return to claim it there,
>given that we have no income from NH?
On the facts presented, the house in NH can reasonably be considered as a second home (as is a vacation or seaside home) and the taxes paid can be claimed on Schedule A.
If you ever do rent the property, however, previous years deductions of tax would possibly/probably be questioned.
On your second point, since you have no income from NH, it would be pointless to file a tax return. (Besides, isn't NH one of those states with no personal income tax? I believe they tax only interest and dividends of residents.)
Bill