No they are not required to withhold them but it is your responsibility to file & pay them.  I am sure if it was required then ADP would be doing so. 

There are a few of issues with that.  1. they paid all of these taxes with the previous payroll software. 2. they with held the local taxes since July 2016 and just last week told me that they can't figure out how to make the software work to pay them.  and 3. IB28 section VII Indiana IRS document outlines guidelines on employer responsibility and as I read it they are responsible in my particular case due to them having a business entity in Indiana. It is a bit vague and  I can't seem to get any clear answer from the Indiana IRS.  They keep saying talk to your HR department.

Seek local assistance with this issue ... contact ADP and your employer ... I think the employer just doesn't want to pay for the extra state withholding if you are the only one.

Do not rely on ADP when it comes to local taxes.  I have been working in payroll for many years and went round and round with them last year, because they were leaving withheld local taxes off of employee w-2s.  They tried to tell me that we did not have to report the local tax withheld in those localities, which is absolutely wrong. In the end they finally admitted that they were wrong and fixed the issue.