I need a piece of advice.
I found an interesting postdoc position one month ago. I applied all required documents (CV and cover letter) and 4-5 days later I was interviewed by the group (including head). A few days later I was asked to prepare the research highlights and I did that. One week later they asked me to apply for the position via the university website if I am interested in the position, and also requested recommendation letters from possible referees. All letters were provided as I know, and they are positive. Moreover, I know I well match to that position. Of course, I do not exclude other possible existing candidates for the position and I can be not the first among them, of course. So, one month passed from the interview.
I haven't experience in the application process for a postdoc position in the US and this is for the first time for me. Thus, the evaluation and hiring process for a postdoc position is a bit unclear for me. I am not sure that a direct request to the lab head for clarifying the situation is a good idea because in this case, I can look like a hysteric or in need person, and I don't want that due to obvious reasons. I do not exclude that they must prepare for the position a justification or something like and this also needs time.
In accordance with the above, I need a piece of advice. What should I do? Is the situation normal or I'm screwed? What should I choose as a strategy (wait or write)?