No, its an evergreen. Looks like its dead, but scrape back a bit of bark near the base to see if its green. Looks like it died from a shortage of water - although they do well in sunny, dry situations, all new plants need a good soaking every few days until they've established good roots, so you'd needed to have watered during dry spells until winter comes.

A thriving rosemary bush indicates that the woman of the house is in charge.

Has there been regime change in your domestic arrangements?

lol