Assuming you are using AISC 341, SMF connections are required where the lateral force resisting system(LFRS) occurs. Beam and column outside of the LFRS do not require SMF connection. Connections that are part of seismic force resisting system (SFRS) have additional requirements see section D2. Column splices not part of SFRS have additional requirements as well.

Quote (Aaron)

do the connections used for the non-seismic beams and columns have to be shear or can they be moment connections

I think that they ought to be shear connections if possible. Otherwise, the moment frames that they create accidentally will:

1)increase seismic base shear for the building.
2)change the distribution of lateral load throughout the building.
3)delay the development of a yield mechanism in the global lateral system.

That said, everything is subject to judgment and scale. If the moment connections you want would create moment frames of negligible stiffness relative to the SMF, so be it.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

If you mean non-ductile by non-seismic, you should not add them to your system. If you do so you have to design the system as OMF.

I wouldn’t mix compliant and non-compliant moment frames. I would think the non-qualified welds could break loose when undergoing the same movement as the special frames.

If the moment connections are part of the gravity only framing system (i.e. cantilever beams supporting cladding), then you could probably design them as non-seismic. However, I would think you would want to provide some detailing to ensure that they do not significantly participate in the lateral force resisting system. In particular, I'm thinking of providing a back span beam to support the cantilever beam. In this way, you are not really relying on the lateral resistance of the column to resist these gravity loads.

It's tricky though, there's some deflection compatibility questions going on. If your gravity system has significant lateral stiffness to pull load out of your lateral frames then I don't see how you can get around detailing it as non-seismic.