Insurance policies are not generally written for blanket coverage unless you are buying some sort of commercial policy. For individuals, each policy is written for the specific piece of property, whether it is a condo, a home, or a car. The premiums you are charged for the coverage you buy will be calculated using a specific address, even for car insurance, and the crime rate for that zip code will play a part in setting your insurance costs. Because of that, you cannot buy liability coverage for one property and extend it to another property.
The exception to the one policy - one address rule is when you purchase an umbrella policy. Umbrella policies are broad liability insurance policies that cover a wide range of property, including your home, car and sometimes secondary property or income-earning dwellings. Not all umbrella policies are created equal, so be sure to verify with your insurance company that the umbrella policy will cover your home and condo before you buy. Umbrella policies are used to increase your total amount of liability coverage, and usually require that the insured property is already covered by another form of liability insurance. The umbrella policy is in addition to the regular liability insurance, but only goes into effect when the regular policy has reached its claim limits.
Buying liability insurance for your condo is not as difficult as you may think. If you start out by getting a free online insurance quote from a website like this one, you can tailor the policy for your needs and desired deductible, and then compare the premiums between multiple companies without having to go to different websites. Shopping online can save you money and time, but keep in mind that you will receive additional discounts if you purchase your new liability coverage from the same company where you purchased other insurance policies.