The signs technically say no dogs allowed; I would think this applies to all dogs, regardless (other than service animals, of course).
I'm sorry but I can't help you I have never been
Ive seen a couple people with tiny dogs in there pocket book
No pets are allowed.
I haven't seen anyone bring dogs in their bags at the Market. There is a "No Dogs Allowed" sign. Maybe you could ask someone at one of the main booths to be sure or contact their website. The only dogs I've ever seen there are Service Dogs and we go almost every weekend. I would check in with someone.
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