Usually, direct objects are in accusative. When the verb gets negated, the accusative is replaced by genitive. Some verbs use different cases for their direct objects, like genitive for nienawidzić, słuchać, oczekiwać, bać się, dative for przyglądać się etc.
Dotykać is also one of those verbs which usually have the direct object in genitive.
There are no hard rules about which verb takes what, you just have to learn them. Just remember that accusative is the default and there are exceptions.
I am touching your hand - Dotykam twoją rękę (Acc) - Dotykam twojej ręki (Gen). Although the second one is correct many nativespeakers would say that the first one is correct as well or even the first one is the only correct sentence.
It is similar to Brazilian Portuguese where spoken language is more flexible and forgiving. The question is: Are we learning proper Polish ONLY or also conversational/spoken Polish?
I don't know exactly about other languages, but although in Polish some forms are often considered correct by a lot of (if not most of) people, we tend to be very conservative about it. For example, when you read or hear colloquial language, you will most likely see tą in accusative feminine, paradoxically enough, much more often than the correct form tę. The same is the case, for example, with plural genitive of mecz (wrong - meczy, correct - meczów). The fact is people here are very sensitive and responsive to it. And I'm not talking about some educated high-class people but, really, all kinds of them. You can talk with someone even clearly dumber than you and when you make some slight minor language mistake, you can often be corrected by them, because they've been already corrected by someone else.
In my opinion, when you learn a language, you should always learn correct forms and rules and be aware of some possible colloquial-speech mistakes, not to be confused by them later. Imagine you learned English like I ain't never gonna do dat because some people may speak it like that, rather than the correct expressions.
Btw, for ones that disagree about the genitive with dotykać (first google result):
This just shows that the Polish I learned as a child 80 plus years ago was not the language as it's spoken now. I went to a Polish school and was taught by sadistic nuns:-) and this was what we learned at the time. Dotykam I did not ever hear until this lesson. Once again, dzieki.
In that meaning it is presently used probably only in fixed phrases: "nie ruszaj" or "nie ruszać" (do not touch, do not move).
The actual meanings of "ruszać" are:
- to start moving in given direction; to begin a journey or ride
- to change the position of something as result of touching it
- to make a movement with some part of one's body
- to begin some activity, to start operation
- (colloquial) to whittle some resources away
- (colloquial) to remove someone from his position
- (colloquial) to start to handle something or someone; to start addressing some problem
- (colloquial) to cause some strong emotion