The state has approved the town’s property tax rate for fiscal 2012, increasing it by 39 cents. That translates to an extra $380 for the average homeowner, according to deputy assessor Mary Quill. She said the new tax rate is $11.98 per $1,000 of property value; the old rate was $11.59. The average single-family home is assessed at $857,800, she said. The state also approved an increase of about $25.5 million in total value of property in Cohasset, with much of the additional value coming from new development in town, Quill said. She said the new tax rate is reflected in the property tax bills mailed last week and due Feb. 1.