This poem rhymes.
If you're expecting more than that, then you're welcome to join me in disappointment alley. The rhyme scheme is AAa, with two of the four tercets ending in slant rhyme. Not only are the repeated rhyme words used in identical ways, but their entire lines are redundant:
It rained the whole time we were laying her down;
Rained from church to grave when we put her down.
The suck of mud at our feet was a hollow sound.
To top it off, the slant rhyme is a stronger, more demanding sound, i.e. less hollow. And the content is handled just as poorly as the form. For example, one can "put down" an animal, and the phrasing of L2 carries that connotation, though unsuccessfully. A simple rearrangement could fix that though:
It rained the whole time when we put her down;
Rained from church to grave when we were laying her down.
I have to wonder, did the poet misuse her words or not even realize the effect they would have?