This is very broad and not clear, can you be more specific? Where state are looking for DL? California has a plethora of DL schools! "State approved" was a term once used in California but not in other states.
I suppose not for CA anymore... I can't seem to find the old BPPVE school database online, but this link contains a list of those schools who qualify/qualified to enter into an agreement with the CA Department of Consumer Affairs that says they will follow the then current CA education code on July 1, 2007: http://www.bppve.ca.gov/forms_pubs/voluntaryagreelist.pdf In my opinion, the schools that said yes are the better schools. As to who offers distance programs, that isn't on the list. Perhaps if you could state the academic discipline and degree leve you seek, the folks on this board could make some suggestions from memory.
There are VERY few distance learning Bachelors degree programs in Engineering (regardless of the sub-specialty). Let me prowl around a bit and maybe I can come up with something.
Here in the United States, and in many other countries as well, a civil engineer is going to need a license. And it might be very difficult to get a license with an unaccredited engineering degree. Most American states will probably require an ABET-accredited degree. So your first item of business should probably be to consult with your local engineering licensing people, wherever you live, to determine what kind of educational qualifications they expect from engineers. I can't really think of any unaccredited civil engineering bachelors programs that I could recommend, certainly none that are delivered entirely by DL. Do you have some reason for inquiring about state-approved degrees specifically? I'm wondering whether you live outside the United States, English isn't your first language, and 'state-approved' is your way of trying to communicate what an American would use the word 'accredited' to say, meaning fully-recognized by all the proper authorities, not a mill, etc.
Not all civil engineers need to have a professional license, only those who sign off on legally required documents need to be a PE. There are many good jobs available in CE where a non-ABET degree or technology degree is useful –including CAD users, site engineers, proposal writers, and laboratory technicians. I would not recommend a state approved degree in engineering – you will find its usfullness very limited While not a "state approved" school the regionally accredited TESC has a BSAST in Civil Engineering Technology http://www.tesc.edu/3185.php Here is an RA university that offers an ABET BS in CE http://www.conted.und.edu/ddp/dedp/
To my knowledge, the only ABET-accredited DL civil engineering BS program in the US is at University of North Dakota. However, there are two drawbacks to this program. First, it requires that you travel to UND every summer to complete the lab requirements, which cumulatively require several weeks of residency. Second, the program can be very expensive if you are not from North Dakota, or some other western or midwestern state. It's 135 credits, and the non-resident tuition rate is around $800 per credit, which totals over $100,000 (not including costs for annual travel/lodging to complete the labs in North Dakota). The TESC BSAST in civil engineering technology is a "technology" degree, not an engineering degree. Graduates will be qualified to assist civil engineers on projects, but the BSAST degree does not have the same legal status or prestige as an ABET-accredited engineering BS degree. It's a better fit for drafters, field inspectors, lab techs, etc., as suggested above. The Penn Foster associate's degree in civil engineering technology is also a "technology" degree. It is only a 2-year degree, so it has more limitations than the 4-year TESC BSAST degree. US schools don't normally offer AS degrees in engineering. You can get AS degrees in engineering technology, like the Penn Foster degree described above.