In Kenya, there is the process of identification of suitable candidates. The candidates are then evaluated by the appointing authority (The Head of state). Once the executive is satisfied, They are then subjected to further assessment by the legislature (parliament and Senate) both on technical issues related to the sectors they will be responsible for. and on personal/social issues. In some instances the legislature may reject the nomination and give reasons. This is the closest to an interview process political appointments go through. For all other public servants at high levels they go through a more rigorous recruitment process that is open to public participation through memorandums etc.

Ghana. 

The procedures described by Andrew are similar for ministerial appointees.

Ghana

I am not certain if this qualifies for what you had in mind, but in the US, there are many appointments made by the president which require the "advice and consent" of the US Senate before the nominee may take office.  This has been done, in the past, primarily as a formality to help senators understand the nominees' backgrounds, for which they may chastise them, but unless something shocking is revealed, approval is generally all but guaranteed, even by the minority party.  If something too embarrassing is revealed, the nominee (in the past) might withdraw before a vote by the senate.  However, we have found that the new US president has appointed people who, like himself, seem to have no such scruples.  Voting for such nominees has now then become much closer, and alarming information has been brought to light. 

The whole system of Government in the US seems to have become broken, which is a much bigger discussion, but at least the investigative process of "advice and consent," required with regard to many, though unfortunately not all, major political appointments by the president, has revealed some of the most troubling information about the new administration.  (It has also revealed that a lack of honesty and an abundance of other human failings, including willful ignorance, appears to infect too many people, though still a minority, which minority seems to have hijacked the US Government from an often dismayed majority of people.  The process of Senate approval has revealed that at least the function of bringing some issues/facts to light still works, though not a lot might be done about it, as the normal mechanisms for controlling someone with authoritarian leanings have been found to often be norms rather than actual laws, and the new administration seems to care little for such norms of acceptable behavior.)

 Concerning some countries which do conduct interviews to the political appointees, I have this view.

In Rwanda, President Kagame does some inquiry to the appointees. This is critical important. I hope reasons for the interviews have been very well narrated in the article by Norman King(2016).  It is my hope that Presidents should do some interviews to ensure preciseness on the appointees. This could be done even without having a clear law on the same.  Kenya is among the very few countries noted, which has clear laws and guidelines that political appointees especially on the Judiciary part and the executive wing must undergo an open interview prior to confirmation.

This has attributed to enhanced performance of the government and thus transparency. People appreciates the performance of the government. It provides respect to them as they get into power through competence based credentials. 

Thanking you in advance,