Can you replace a CR1220 battery with a CR2032?

Most likely not (No). They are the same voltage, but not the same size. The following specs are from Duracell's web site: google&utm_medium=cpc&utm_term=%2BCR1220%20%2Bbatteries&utm_campaign=Duracell_Search_Desktop_Category+Interest|Electronics+Batteries&utm_content=s95QccF16_20317950700_b_%2BCR1220%20%2Bbatteries:">http://www.duracell.com/en-US/series/electronic-batteries.jspx?utm_source=google&utm_medium=cpc&utm_term=%2BCR1220%20%2Bbatteries&utm_campaign=Duracell_Search_Desktop_Category+Interest|Electronics+Batteries&utm_content=s95QccF16_20317950700_b_%2BCR1220%20%2Bbatteries:

• IEC: CR1220
• 3.0 Volt
• 35 mAh
• Size (mm): 2 x 13 x 13
• Lithium

Now compare that to:

• IEC: CR2032
• 3.0 Volt
• 220 mAh
• Size (mm): 3 x 20 x 20
• Lithium

The mAh is milli Amp hours, which measures the strength of the battery against a load (how long it can last). The CR2032 is a bigger, stronger battery. I didn't know that before today.