Some people have what is called "dual fuel" for heat -- both a combustion fuel and a heat pump.  Note that while technically the "backup" strips are a "dual" fuel they're really not since both are electricity -- and resistance heating is the worst choice.

The question thus arises "at what temperature outside should I set the unit to change over?"

This is a math problem; the general formula is found on this page.

You need to know (1) your kilowatt-hour charge for electricity, (2) the cost for therms if you have natural gas (or the cost-per gallon for propane; each gallon is 0.916 therm), (3) the efficiency of your gas furnace (0.80 is typical for old-style non-condensing, 0.90 to 0.95 for the newer condensing furnaces) and you need to find the chart in your heat pump's installation manual (if you don't have it, get the model number and look online) that gives you the COP, which is Coefficient of Performance curve for various outdoor temperatures, indoor coil input temperatures and airflow.

With the indoor coil you have you can determine the airflow setting in use, or if you don't know use the middle one -- it'll be pretty close.

So here's an example:

Electricity costs 0.15/kWh
Natural Gas costs $1.35/therm
Your furnace is new (95% efficient)

Therefore the COP changeover point is: (0.15 * 0.95 * 29.3) / 1.35 = 3.09

Now look on your chart or table for your heat pump and find where the COP for your typical conditions indoors (usually 70F at the coil) and airflow (if you know, or use the middle if you have to guess) crosses 3.09 for outdoor temperature.

Above that outdoor temperature the heat pump is cheaper to run, below it the fuel is cheaper.

That is where you set the changeover.

Note that as the power or fuel cost changes so does the proper change point and most of the time that's reasonably stable during a winter season but changes from year to year, possibly by quite a bit, especially for either gas or propane.  Also note that with propane being wildly more expensive than natural gas most of the time the difference between those two alternative fuels is huge if the power cost is identical.

This is all a numbers question and if you can use either at your discretion why would you spend more money than you need to keeping your house warm in the winter?

Calculate the correct place each fall, set that, and whenever the power or fuel cost change get out the calculator and see if you need to move it.

You might think that dual fuel makes no sense up north but you'd be wrong; it in fact makes more sense up north than it does anywhere else because up north there are very significant parts of the year where a heat pump wins big on operating cost but at the same time it gets cold enough that it can be a huge lose, especially if you size it sufficiently to be able to keep the house warm at all in cold temperatures.  Most modern systems will produce quite a bit of usable heat even at zero Fahrenheit outdoors but they usually lose massively to natural gas at that temperature as their COP is down to 1.5 or so.  At 40F, however, modern units can produce a COP of 3.0 which can be a huge win, especially against propane.  In fact if your secondary fuel is propane the heat pump is often cheaper to run, depending on electrical cost, even down into the single digits outdoors!

This is a math problem so run it for your unit and see where the correct place to set it is.  If you're looking to replace an HVAC and have a secondary fuel available run some typical scenarios -- you might be surprised at how fast the dual-fuel setup pays for its additional up-front expense and the further north you are and thus the larger your "shoulder" season the more-likely that is to be true.