Something similar happened to me on my first flight after getting my PPL.
Proudly took a friend to the airfield and loaded him into the PA28. A few minutes after take off the announced he was getting wet (we were passing through a small shower) - sure enough the top latch hadn't engaged. After a few seconds, since:
- I remembered being told it wasn't an emergency if the door came open
- I couldn't remember what the book said I should do
I told my friend that a little bit of water wouldn't hurt him ... and left the door alone until we landed.
From the PA38 POH:
If both upper and side latches are open the door will trail slightly open and airspeeds will be reduced slightly.
To close the door in flight:
Slow airplane to 90 KIAS
Cabin vents....................................................... ..............................................close
Storm window...................................................... ............................................open
If upper latch is open........................................................ ................................latch
If side latch is open...............pull on arm rest while moving latch handle to latched position.
If both latches are open...................................................latch side latch then top latch
Simples
OC619