When you inherit a share of a house in the state of Massachusetts, is there a tax on it? The share of the inheritance is under $70,000.?

MA does not have an inheritance tax, so there's nothing that you need to do for your 2015 taxes unless you sell it before the end of the year.

When the property is sold, you will pay capital gains tax on the difference between your share of the basis in the home and your share of the net proceeds from the sale. The basis in the home is the value of it on the date of death of the decedent. Any gains on inherited property are taxed as long term capital gains regardless of the holding period.

If you or your siblings live in the home for 2 of the 5 years immediately prior to the sale you may be able to exclude some or all of the gain from taxes.

If the property is rented out, get professional assistance. You will need it, now and when you sell.

Normal property tax will be due.

yes