Is there any tools to test, whether the set of co-expressed genes in microarray study are also co-regulated or not?
I tried ChEA to find the TF of co-expressed genes, but it was not rich database for microRNA.
Answering your biological question, there are some chance of some genes being regulated by the same transcription factors set to be co-expressed, some times this pattern it's very sharp in particular when you expect a non-return control point (like development or cell-specificity). In general this pattern is really noisy, several genes controlled by the same TF barely conserve a co-expression because you know, there are other levels of regulation (transcription rate, mRNA stability, protein modifications, ...). Therefore a lot of strong statistical tests are required and bench validation.
So, if you define your co-expressed genes as clusters (or using something like k-means clustering), this is meant to address your type of question. I believe it provides both upstream and downstream motifs. There are other similar tools, but this is what I can think of off the top of my head.