No, unlike something like a firearm which you are legally required to secure and can suffer potentially criminal and/or civil liability if someone steals it and uses it to commit a crime, there is no such legal requirement to secure your network against outsider misuse.
IANAL that’s just my personal understanding / belief.
The key point would be the use would have to be unsanctioned and you were totally unaware. Once you give someone your WiFi password, it’s less clear if you have any liability. I’m not sure of any case where the actual user was known but the person who provided the network connection was blamed.
Network access is fairly universal. The particular method used to access the Internet is practically irrelevant. The actor and the act are what is important, not how the packets are routed.
I believe the legal term you’re looking for is “strict liability”.
Many states don’t actually have laws about securing firearms directly but have a concept of strict liability about what happens if they are stolen, or stolen and not reported.
Have a look through your ISP's terms of use and you might find specific relevant statements there. Operating an open-wifi Internet access setup might be difficult if your ISP terminates your contract.
An example, this is from Verizon[1]
2. Use of your Service and Account and Compliance with Applicable Authority. You are responsible for all use of your Service and account, whether by you or someone using your account with or without your permission, including all secondary or sub-accounts associated with your primary account, and to pay for all activity associated with your account. You agree to comply with all applicable laws, regulations and rules regarding your use of the Service and to only use the Service within the United States (unless otherwise permitted by this Agreement).
3. Restrictions on Use. The Service is a consumer grade service and is not designed for or intended to be used for any commercial purpose. Except as otherwise set forth in this Agreement, you may not resell, re-provision or rent the Service, (either for a fee or without charge) or allow third parties to use the Service via wired, wireless or other means. For example, you may not provide Internet access to third parties through a wired or wireless connection or use the Service to facilitate public Internet access (such as through a Wi-Fi hotspot), use it for high volume purposes, or engage in similar activities that constitute such use (commercial or non-commercial). If you subscribe to a Broadband Service, you may connect multiple computers/devices within a single home to your modem and/or router to access the Service through a single Verizon-issued IP address, and if available through the Service, you may permit guests to access the Internet through your Service’s Wi-Fi capabilities. You also may not exceed the bandwidth usage limitations that Verizon may establish from time to time for the Service, or use the Service to host any type of server. Violation of this Section may result in bandwidth restrictions on your Service or suspension or termination of your Service.
IANAL that’s just my personal understanding / belief.
The key point would be the use would have to be unsanctioned and you were totally unaware. Once you give someone your WiFi password, it’s less clear if you have any liability. I’m not sure of any case where the actual user was known but the person who provided the network connection was blamed.
Network access is fairly universal. The particular method used to access the Internet is practically irrelevant. The actor and the act are what is important, not how the packets are routed.