Here is a preprint on a serological test for SARS-CoV-2 across multiple animal species. This test can be used to determine if a pet (or any other animal) has had Covid-19.
Here's how it works. The receptor binding region of the virus (portion of the spike that binds to cells to start the infection) is coated in a plate (test device). Serum from the possibly affected animal is added to the plate and any antibodies against the SARS-CoV-2 spike protein binds to the material coated on the plate. The excess serum is washed out and a species specific detection antibody is added to the plate. Any antibodies that bind to the SARs-CoV-2 material in the plate AND is the same species as the detection antibody will produce a titer signal. The same titer plate can be used for any species; only the detection reagent needs to be selected for the species being tested.
Multi-species ELISA for the detection of antibodies against SARS-CoV-2 in animalsI forgot to note that this is of interest to the medical community to enable determining what animal species might become reservoirs for this virus.