What dehumdifier do you have? How is the condensate pump connected to the dehumdifier?

Dehumidfiers are usually built to shut themselves off when the water reservoir fills up. Does yours have this feature?

Yes it does have that feature, I think they all do. Mine has a hose attached. That hose drains by gravity to the condensate pump. The pump must be below the dehumidifer for this to occur. If the pump fails the pump resivor will overflow. There is nothing to stop the flow of water at that point, therefore the humidifier tank float will not trip.

What voltage is the overflow from the pump?

That will determine the relay coil voltage.

The AC load of the dehumidifier will determine the required contact rating for the relay.

You would put the relay in a small junction box with a cord to plug into the wall and a receptacle for the dehumidifeir.

The relay contacts go in series with the 'hot' line from the plug and the receptacle.

You need to make sure any low voltage wiring (possibly the overflow line) is isolated from the 120 V AC wiring powering the receptacle.

If you do not have any real experience with this type of thing, try to find someone who does to help.

It is not hard, just needs attention to details to operate and be safe.

Condensate pumps usually have a 24 volt outputs in order to make them compatible with HVAC systems. If your pump has a alarm output it could be used to energize a relay. The relay would have to be normally closed and be able to switch a 120V line connection large enough for your humidifier. Humidifiers can pull a 5 - 8 amps of current depending how big they are. It may be difficult to find a suitable relay.

There are inexpensive water alarms which go off if the water level rises. It won't shut off the dehumidifer but at least you will hear the alarm when you are home. You could sit the pump inside a basin and attach the alarm to the basin.

I found a disconnect which you may be able to use. It is expensive but it is all self contained and should be easy to wire to your condensate pump.

Check out the link and the You Tube video.

Here is a link that might be useful: Automatic Dehumidifier Disconnect Flood Prevention System

"Condensate pumps usually have a 24 volt outputs in order to make them compatible with HVAC systems."

I would have guessed that they use dry contacts to break or make a circuit.

What's a dry contact?

If the condensate pump safety is dry contact, and you can get to the switch inside the dehumidifier, you might be able to disconnect the internal switch and hook the dehumidifier circuit to the condensate pump. Be careful to analyze both devices carefully before you try this. You could easily release smoke from your equipment and render it inoperable.

"What's a dry contact?"

Just a switch, no voltage, no current until you hook something to it.

I am not following how your suggestion would work. The dehumdifer operates on 120V only. The condensate pump has a 120v input and 24V outputs. You need an interface to make them compatible.

If the dehumidifier has a low-voltage, NC float switch, intercept that circuit and connect to the NC dry contacts that are typically found on the condensate pumps.

If you have 24V native to your condensate pump, you have a very unusual condensate pump.

Such complicated non-answers - mostly from people that don't even get the problem. The Jackson ADD switch was THE answer, but it is extinct. The solution (Now only $26) is this switch that hooks up directly to the condensate pump, and you plug the dehumidifier into the outlet. It is like a power strip with input from the 2 wires from the pump. https://www.amazon.com/gp/product/B00WV7GMA2/ref=ppx_yo_dt_b_asin_title_o01_s00?ie=UTF8&psc=1