When is ok to ask for an update?

Hi y’all.

I’m wondering at what point I should reach out to a hiring manager to see if I’m still in the running.

Three weeks ago, I interviewed for two different positions in different agencies. Afterwards, both asked for references and then started contacting them the following week. Since then, it’s been ~2 weeks and I’m wondering if I should follow-up. I know the process can be slow, but both mentioned they hoped to have an answer by last week.

Was thinking I would email them if I don’t hear back this week, but don’t want to seem impatient. Any recommendations on what’s best would be appreciated!