Is there a limit for the attachment size in Messages?

I'm trying to send a 36 MB .mp4 video via Messages, but I'm not exactly sure if it's working.

After sending the file, the CPU usage of the processes VTDecoderXPCService and IMTranscoderAgent goes up very high (~300%) and then only about 11 MB of data are send.

I doubt that Messages is performing some magical compression that results in <30% of the original video file size for the transfer, instead I assume that the whole file is not send. But I'm not receiving a warning such as:
"Could not transfer file. Attachment too large..."

Is there a limit for the attachment size in Messages?

Despite Joost's links, Apple did officially provide a size limit for Messages attachments.

Extracted from Mountain Lion's Features page:

Send large attachments: Send high-quality photos, full HD video, or documents. iMessage allows attachments of up to 100MB.

Your 36MB file is, indeed, off the limit.

It seems Apple has not documented this properly. Some articles show that 220MB is over the limit and that it's most likely between 101.4MB and 194MB

In either case, your 36MB file should not be hitting any limits. That means there must be something else going on.