There is no such thing as “64-bit file format”. So, if you work on same file on either 32-bit LO, or 64-bit LO, the saved file would be identical and openable on either bitness.
On Windows, all 4.x and earlier versions of LO were 32-bit, so no need to guess. However, since 5.x, Windows 64-bit versions have this data in Help-About (like Version: 18.104.22.168 (x64)). Anyway, if you run 32-bit Windows software, you may find that out by using Task Manager which shows that information next to task name.
Having said all the above, it’s not guaranteed that any file saved with 64-bit LO would definitely open with 32-bit one. This is because 64-bit LO can use more than 2 GB memory, and thus documents which require that much memory would open in 64-bit LO while fail with 32-bit one. File size doesn’t actually matter. Here is a sample file that takes only 141 KB, but requires 4.7 GB in memory (it has no data, just 10000 empty sheets).
This isn’t a bug, it’s just the reason to use 64-bit version, that exists mainly for the purpose of being able to handle more data. The 64-bit architecture is just about that. Limitations of 32-bit systems are actually limitations. Of course, something could be improved in LO to allow smaller memory usage in some scenarios, but whatever would change, there will always be documents that require more than 32-bit systems may handle.
Another note: even files saved in 32-bit version may fail to open in 32-bit version due to insufficient memory, and require 64-bit LO to open. This is because when file is read from disk, the program creates temporary memory data used for import only, and freed after open completed. So, imagine a file that is OK for 32-bit, but large enough. It is opened in 32-bit, and memory usage was, say, 1.7 GB during opening, and dropped to 1 GB after opened. Then the file is edited, and more data added, so edited memory usage is now 1.4 GB. Then the file is saved, and save completes successfully (memory consumption during save temporarily rised to 1.6 GB). If you will try to open this file again in 32-bit, you’ll need memory more than available for 32-bit (during opening phase: like 2.1 GB), even though it would require only 1.4 after opening. This situation happens from time to time, and that’s something to take account for (see e.g. this question, where it was exactly this problem - found out after private consulting).