In many jurisdictions they do, yes. A general guideline is that if it requires an permit it will typically trigger an assessment and thus increase in property tax

If everything else is equal, a roof replacement or other maintenance shouldn't appreciably change the value of the house (not beyond the cost of maintenance).

What WILL change your property tax is an addition or similar that makes your house go from X (same as everyone around you) to 1.2X or similar, then you'll proportionally pay more tax.

(It varies by district, but most USA property taxes are calculated by figuring out the budget for the city/county/school district, and dividing it proportionally amongst the valuations of properties/houses. This is often displayed as a percentage of the value, but it is not a percentage TAX - as if everyone's property doubles overnight but the budget remains the same, the property tax dollar amounts would remain the same while the percentage reported goes down.)

Depends on how your locality assesses the value of your home. You can probably do a web search for where you live specifically if you want to get into the nitty gritty. In the places I've lived, unless I added more square footage, these won't trigger an automatic property tax increase.

But if the improvements on your house makes the neighborhood more desirable and your neighbor's house sell for a higher price then your locality expects, then your house will be assessed at a higher value the next time the locality does their assessments, which means higher taxes.

Of course, improvements to your home that increase a sale value will affect the taxes, but the buyer has to deal with that.

Do some localities assess homes individually every so often? I wonder...

In general a roof repair (including a full replacement) won’t trigger a re-assessment but a kitchen remodel will.

A roof replacement isn’t really an improvement so much as expensive maintenance.

Imagine actually telling the government that you remodeled your kitchen. Nobody is that dumb, right?

Some people think the primary purpose of building permits and inspections is to ensure quality work. Others disagree.