To answer the first question No a duplex can not be constructed in an area zoned for single family.
The follow up question raises many other questions. Is the "use code" on the tax records shown as "duplex"? If so then it is legal - non-conforming, if the use code shows single-family and it is being sold as a duplex or as an in-law or any other division of property the listing agent is likely making an error.
A number of issues surround the plethora of "un-warranted" units in the City. While the City turns a blind eye to them because they provide a large inventory of affordable housing units many neighborhoods are strongly against them.
If you are buying a property that has a use other then is shown be aware that you are buying a possible problem. If the City decides that it no longer wants to ignore them for any reason you would be on the hook for abatement or reconstruction to the current building codes. While it is unlikely that City would destroy them and turn all the residents out it is very possible that they could hunger for the fees that they havenâ€™t collected for permits and back property taxes.
Another issue that is currently being seen is the Cityâ€™s reluctance to remove units from the housing stock through merging property. If there are multiple units in a property the City doesnâ€™t want them to be merged. A case in point would be a single family that had an in-law unit added, for example during the war years when a number of in-laws were allowed to relieve a housing crunch. It might be legal â€“ non-conforming but if you went for permits to merge the property youâ€™d get resistance from the building and planning departments.
So if you are buying a property and have questions like this you would be better consulting an attorney and short of that do research beyond Realtors, like go to the building department with documentation and ask questions.