just re-watched it again, and here is my opinion.
during the shootfight on the beach, i guess the bad guys didn't know he was not alone, and if you pay attention, when Rika escaped to the car, lights are not on her, so they didn't see her leave. they possibly followed then from far that's why they discovered the relationship between the two.
Riggs thought the best way to secure her was to make like nothing happened she would go back to work on the next morning giving a resignation to Rudd
just my two cents looks plausible
anyway, love makes people take dumb decisions at a time !!

a French Guy

None of the shooters see Rika, so it makes sense within the film that he'd think they wouldn't have any way of knowing she was there.

Good question. Many action films have plot holes but this is larger than most.

She worked for them. Maybe he thought she was safe.
She was a (hot as hell) dumbass who should have said "Don't leave me here, you moron"

Still didnt have to kill her off. She could have got a job offer back in South Africa or Europe

I always thought that was pretty ignorant of him
I don't mean to impose, but I am the Ocean.

LOL! I always wondered the same thing
Prostitute: What the beep are you doing?
Johnny: I'm gonna kill a bunch of people.

It is a HUGE HUGE HUGE plot hole in the film. The first time I saw the film (back in '89), I wasn't really paying attention. I just watched it again for the first time in years tonight and I came on IMDb to ask about the very same thing.
Riggs KNEW the armed assassins in the helicopters who were trying to kill him in his trailer on the beach were the South Africans!!! Yet he took Rika and dropped her off at her apartment, KNOWING THEY KNEW WHERE SHE LIVED!!! What the hell was he thinking (or not thinking)???
That's what you call lazy scriptwriting. I don't buy - for an instant - that it's because they wanted Rene Russo for part 3. Hell, part 3 was still three years away (!). Is there even any evidence that when they were making this film, Richard Donner knew he wanted Rene Russo for part 3? If he did, why not put her in this film and have her be the love interest instead of Rika? It doesn't make sense.
It's just lousy scriptwriting. Pure and simple. Riggs should've NEVER dropped Rika off at her apartment. A seasoned cop should've known better.
Otherwise, it's still a fun shoot-'em up action film.
"You can dish it out, but you got so you can't take it no more." - Caesar Enrico Bandello

Because that would have been boring.
Cult Leader my mind's frightening, I drink blood from a human skull like a Viking

in the pure lethal documentry rika did originally survive as she was in the alternate ending chasing a turkey with riggs and the murtaughs but richaard donner said for the sake of riggs character the decided she had to die on a lighter note after seeing her topless i had a sudden desire for fried eggs

Because Danny Glover stated in an interview that the producers and directors wanted Riggs to be with Lorna instead of Rika so they had to kill off Rika so Riggs could meet Lorna in the 3rd movie
Really? Wonder why they wanted that Lorna isn't anything special either.
I don't mean to impose, but I am the Ocean.

interesting.
Where there's smoke, there's barbecue!

This message has been deleted.

Because Danny Glover stated in an interview that the producers and directors wanted Riggs to be with Lorna instead of Rika so they had to kill off Rika so Riggs could meet Lorna in the 3rd movie which I think is stupid because I think Rika was a better 2nd Mrs. Martin Riggs instead of Lorna but that's just my opinion. Now ya get the picture?