Is it legal to bring a dog to work?

It's only required by law for your employed to allow it if it's a certified aide dog - for example, if you'd be blind or significantly disabled. There are certain exceptions to this rule - working in a kitchen, for example - but it's the general rule of thumb.

Any other kind would be subject to your employer's discretion, except for jobs like the one I mentioned above where your local Health Code would prohibit it.