Following up on a state government job offer

I recently received an oral offer to start a state government job. They called last Tuesday, the 16th, to give a formal offer. The start date is not until towards the end of May. Besides that phone call, I haven't heard anything else. They mentioned the state HR department would contact me about going through the security/background check, and that it might take some time so they would be in touch soon. They also mentioned some online orientation that they would like me to complete before I begin.Would it be bad if I followed up with my new supervisor and ask when I can expect to hear from them? Not sure if that would come across bad. Or is it just expected to take a while when it comes to state government jobs?

Thanks!

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