Did dinosaurs have periods?

No, they didn't.

Once a month, one of a woman's ovaries releases an egg. At this point in her cycle, the lining of the womb is thickened so that the egg can embed in it if it is fertilised, and begin to grow. If pregnancy does not occur, this lining and the unfertilised egg are discarded - this is what a period is. Dinosaurs laid eggs rather than giving birth to live young - their eggs were coated in shell and then laid, so they did not need a thickened womb lining for eggs to embed in and thus did not shed said lining if pregnancy did not occur.

In response to your first answer, I'd like to point out that dinosaurs were very different to mammals of today - dinosaurs were reptiles, not mammals - and that mammals like dogs and cats do NOT have periods. They reabsorb the womb lining into their bodies instead of shedding it if they do not become pregnant. When they are in oestrus, they produce a bloody discharge, which may lead some people to think the animal is having a period, but this is not the case - the animal is ready to conceive, not getting rid of its womb lining after failing to conceive.

Nope. Only humans have a period. Other mammals have seasonal reproductive cycles or a variation based on weaning of young, ie higher primates. Fish, sharks, reptiles, amphibians and birds do not have a menstrual cycle.

Menstruation is a characteristic of placental mammals. The inside layer of the uterus is periodically renewed.

Dinosaurs are not placental mammals. They're not mammals at all. So no. The closest living relatives of dinosaurs are birds - which are descended from one subgroup of dinosaurs. The second closest living relatives of dinosaurs are crocodiles (which are archosaurs) - see http://www.dinosaurjungle.com/dinosaur_facts_familytree.php

As you know birds and crocodiles both lay eggs.

I believe dinosaurs were supposed to be a lot like chickens.

In chickens, I think that the ejected unfertilized eggs that we eat are the equivalent of a chickens period in its equivalent to mammalian menstrual cycles.

yes, they did. They were called menstra-saurian cycles. The T-rex had the longest period called the tyrano-cycle. in latin this means, the terrible cycle. it lasted like a month. it used trees as tampons.

No, they didn't have periods.