reflexive verb determining whether "sich" should be dative or accusative

Question

I have gathered the following information from the University of Michigan's German course:

Normally the reflexive pronoun will be accusative. If the verb already has an accusative object, however, then the reflexive pronoun will be dative. Note that you will only notice this difference in the ich- and du-forms, since for all the other persons, the accusative and dative reflexive pronouns are identical.

This seems pretty useful guide for me. Can I take this as a rule when determining whether 'sich' should be accusative or dative? Is this rule really valid?

For example, sich überlegen. This has to be dative because you need to consider something and it already has an accusative object here.

Answer 1

The rule "if there is an accusative, the second noun must be dative" only goes for verbs requiring those two cases. There are others, e.g.

Er schimpfte sich (accusative) einen Esel (accusative), weil er so blöd gewesen war.

so this can't be taken as a general rule.

You can't say that a reflexive pronoun is "normally" accusative, either. It can represent all cases, it's just that they often look alike. The reflexive sich represents a dative whenever the dative is required by the verb or in the context of the sentence:

Ich lasse mich fallen (accusative). Er lässt sich fallen.

Ich lasse mir das nicht mehr gefallen (dative). Er lässt sich das nicht mehr gefallen.

Ich gefalle mir. Er gefällt sich.

Thus it goes:

Ich: meiner / mir / mich

Du: deiner / dir / dich

Er/sie: seiner, ihrer (selbst) / sich / sich

Sich looks the same in both cases, the genitive form would be "seiner (selbst)" and "ihrer (selbst)".

Wir: unser / uns / uns

Ihr: euer / euch / euch

Sie: ihrer (selbst) / sich / sich

If you want to determine if a "sich" is accusative or dative, just transform it to an "Ich" sentence:

Er überlegt sich das. -> Ich überlege mir das -> dative.

Answer 2

The presence of an object the action relies on, an accusative one, forces the reflexive to be dative, as you pointed out. There exist instances where the reflexive pronoun of a verb might be both A and D.

Example:
1. Ich wasche mich
2. Ich wasche mir die Hände

That's the main rule. Some others, secondary, might exist, though.